Gemara

Shtei ha'Lechem are considered to be one unit. If there are not two, it is Pasul.

The verse also calls them two ("Shtayim Shnei Esronim"). Each must be kneaded and arranged by itself.

Chulin 83a (Mishnah): There are four times when one who sells an animal must tell the buyer if he sold its mother or child to be slaughtered that same day - Erev Simchas Torah, Erev Pesach, Erev Shavu'os, Erev Rosh Hashanah.

Rishonim

Kolbo (52, brought in Eliyahu Rabah OC 494:10): Some have the custom is to eat honey and milk on Shavu'os, due to the Torah, which is compared to honey and milk ("Devash v'Chalav Tachas Leshoncha"). We put saffron on Matzah, for it gladdens the heart. Women make a long loaf with four ends to commemorate Shtei ha'Lechem, or because the Mazel (constellation) of twins dominates in Sivan.

Eliyahu Zutah (494:7): Kolbo connotes that the custom is to eat dairy also on the second day. The Shlah says that one should eat dairy, say Birkas ha'Mazon, wait a Sha'ah (literally an hour, but this often means simply a period of time), and eat meat.

Poskim

Rema (OC 494:3): The custom is in every place is to eat dairy foods on the first day of Shavu'os. It seems that this is like the two cooked foods on Pesach night, to commemorate the Korban Pesach and Chagigah, so we eat dairy and afterwards meat, and we must bring two breads on the table, which is in place of the Mizbe'ach, and this commemorates Shtei ha'Lechem that they would offer on Shavu'os.

Magen Avraham (6): There are many reasons for the custom. The Zohar says that during the seven weeks (from Yetzi'as Mitzrayim until Matan Torah) Bnei Yisrael were like a woman becoming Tahor from Nidah. It is known that the blood is withheld and it turns to milk, i.e. from Midas ha'Din to mercy. One must be careful not to come to Isur. He need not interrupt with Birkas ha'Mazon if he does not eat hard cheese. He should be careful to use a different tablecloth (for meat than for milk).

Magen Avraham (8): One may not eat meat and milk with the same loaf. Therefore, the custom is to bake the bread (that he will eat with dairy) with butter, for this forces him to bring another loaf to eat with meat. One must heat the oven (between cooking the dairy bread and the Pareve bread with which he will eat meat) and use a new shovel to remove the bread from the oven. Some women merely turn the shovel on the other side. This is wrong, for the fat is absorbed all the way to the other side.

Magen Avraham (9): Since it commemorates Shtei ha'Lechem, they should be of wheat, like Shtei ha'Lechem.

Eliyahu Rabah (10): Tzedah la'Derech says that milk is the food of youths, because they are tender, and corresponding to this the Torah gives Mitzvos of action, which are food for the Nefesh. Honey is sweet, and a youth cannot accept (eat) it, and an adult can have only a little. The same applies to the true Chachmah of Torah. Shtei ha'Lechem of wheat corresponds to Na'aseh v'Nishma, which are the food of the Nefesh. The Omer on Pesach is from barley, which is (primarily) food of animals, because only the bodies were redeemed on Pesach. Some have the custom to eat cheese at the afternoon Seudah, even though it is less than six hours after the morning Seudah, as long as he cleans his teeth.

Shulchan Aruch ha'Rav (16): The custom is everywhere is to eat dairy on the first day. The custom of Yisrael is Torah. It is a Mitzvah to eat meat on every Yom Tov. One must follow what is says in YD 88,89 (below).

Kaf ha'Chayim (63): If one needs only one loaf of the Lechem Mishneh (to eat with the diary), he should remove the other loaf, lest it get dirty from the dairy.

Kaf ha'Chayim (64): Even though normally one may not bake dairy bread, we permit such cases (YD 96), i.e. a small amount with a different shape. However, he should not bless ha'Motzi on the dairy bread.

Mishnah Berurah (12): I also heard that when Yisrael were on Har Sinai and received the Torah (for all parts of Torah were revealed within Aseres ha'Dibros, like Rav Sadya Gaon wrote), and they descended from the mountain to their homes, the only thing they could eat immediately was dairy. Meat needs great preparation, to slaughter, check, remove the Chelev and blood, i.e. to rinse and salt and cook in new Kelim, for their Kelim that they had cooked in in the last 24 hours were forbidden, therefore, they chose dairy foods. We commemorate this.

Note: all agree that the Torah was given on Shabbos. In any case they could not cook until after Shabbos! A pot could be Ben Yomo if one left food in it on a fire from before Shabbos, like we do nowadays. (They were already commanded about Shabbos beforehand.) Alternatively, perhaps they could have cooked in the sun; the Torah permits this on Shabbos.

Mishnah Berurah (16): One need not say Birkas ha'Mazon in between eating dairy and meat, unless he ate hard cheese. He just cleans his mouth well and rinses.

Aruch ha'Shulchan (5): The initial letters of "(Minchah) Chadashah la'Shem bi'Shavu'oseichem" spells Chalav (milk). One may not be more lenient about meat after milk or vice-versa on Shavu'os than during the rest of the year.

Si'ach Yitzchak (234 DH b'Ezras): In some places many have the custom is to eat only dairy on Shavu'os night. Darchei Teshuvah (YD 89:19) says that some do so in order to fulfill eating meat on Yom Tov, and during the day they eat only a meat meal. They say that this fulfills all opinions. I disagree. Based on Sha'agas Aryeh (66), who says that the Chiyuv mid'Oraisa of Simchah is only in the morning meal of Yom Tov, but at night it is only mid'Rabanan, there is room to be lenient. However, the Magen Avraham (546:4) says that Simchah is mid'Oraisa also the first night of Yom Tov, therefore, one should eat meat also then. A support for those who refrain on the first ngiht of Shavu'os is from Sha'ar Oros, that on Shavu'os night we do not say Torah, for Derech Eretz preceded Torah, and it is improper to say Torah before receiving Torah. An Am ha'Aretz may not eat meat (Pesachim 49b). The Chasam Sofer brings that the cloud covered Moshe to clean out the food in his innards. 'Before praying that Torah enter your innards, pray that overeating not enter your innards.' However, after Kabalas ha'Torah, it is a Mitzvah to be Some'ach. All agree that Shavu'os must also be for you (eating - Pesachim 68b). A hint is "va'Yechezu Es ha'Elokim va'Yochlu v'Yishtu." Chachamim enacted that Seudas Purim must be during the day (Megilah 7b). The custom is to fast the day before, so Kri'as ha'Megilah is like Kabalas ha'Torah with a stomach that is not full, and afterwards is Simchas Purim. However, the custom is difficult, for dairy food induces sleep, and one must stay awake on Shavu'os night (Magen Avraham, from the Zohar).

Divrei Yatizv (Likutim 41 DH v'Chol): To show the greatness of Yisrael on Shavu'os we eat dairy, to show that we do not need meat and wine for Simchah. We are satiated with Torah, which gladdens the heart. The custom to wrap cheese in dough (Kreplach) is to show that "va'Yochlu v'Yishtu" does not mean that they ate and drank, rather, like the Targum, they were happy as if they ate and drank. Kreplach allude to eating what is not seen (what is inside).

Mishneh Halachos (6:135): Darchei Teshuvah concludes that the best custom is to eat dairy at the time of Kidush, wait about an hour after the Berachah Acharonah, and then to eat the morning meal (with meat). Some wait only a half-hour in between. I say that it is better to wait a full hour.

Kaf ha'Chayim (173:2): One who fears Heaven should not eat meat within one hour of milk, and not in the same meal even after an hour, even though letter of the law cleaning and rinsing suffices. One who is stringent like the Ari Zal will not eat meat until evening; he is called Kodesh.

Toras Chayim (Bava Metzi'a 86b DH d'Kama): The Torah does not say that Avraham served butter and milk to the angels, and (then) the ox. The Medrash (Pesikta Rabsi, Aser Ta'aser) says that he served them together. He thought that they are Aravim. Perhaps they like meat and milk. The angels protested that Hash-m should not give Torah to Yisrael. Hash-m answered that the angels ate meat and milk, and a Yisrael child would not do so. Perhaps this is why on Shavu'os we eat dairy and afterwards meat, through cleaning and rinsing and other precautions, so the angels cannot protest each year on the day of Matan Torah.

Toras Chayim (Chulin 83a DH v'Erev): Our Mishnah shows that the custom is to eat meat on Shavu'os. This refutes the custom to eat dairy on Shavu'os. Some do not eat meat at all. The Tana was in Eretz Yisrael, where Yom Tov is only one day (and he says that people slaughtered). Presumably, they slaughtered also for the day meal, like for the other three days. They would prepare a calf for Rav Yosef on Shavu'os (Pesachim 68b). According to all the reasons for the custom, one should eat also meat afterwards. The Zohar forbids this. Therefore, one should refrain from the custom.

Mishneh Halachos (7:70): Darchei Teshuvah (9:19) rebutted this and defended the custom. However, one should not be lenient more lenient about meat and milk than at other times, unless he has a tradition for this.

Igros Moshe (OC 1:160 DH Mah): One need not eat two cooked foods on Shavu'os. If this was needed, this would allude to Shtei ha'Lechem, and we would not need another commemoration! Chachamim did not enact (like they enacted for Pesach), because only Kohanim ate Shtei ha'Lechem in the Azarah, and it was not evident to people even when the Mikdash stood. In any case we learn that it is good to do so. The custom is not to do so within one meal, because some do eat meat at the same meal even if the milk is first. Also, perhaps people will forget and eat the meat first. Therefore, it is better to bless after the dairy, Chak Yakov says that some eat both in one meal, but it is better not to.

Rema (YD 89:1): Some say that one need not wait six hours after meat before eating milk. However, he must say Birkas ha'Mazon in between.

Sifsei Da'as (6): The Acharonim say that likewise, who is stringent not to eat meat after cheese, based on the Zohar, must say a Berachah Acharonah after milk before eating meat. On Shavu'os the custom is to eat dairy, bless Birkas ha'Mazon, and then eat meat.

Shulchan Aruch (2): If one ate cheese, he may eat meat immediately afterwards, as long as he checks his hands that none of the cheese stuck to them. If it is night and he cannot check them well, he must wash them. He must clean his mouth through chewing bread, or anything except for flour, dates or vegetables. Afterwards he rinses his mouth with water or wine. This is to eat beef. For poultry, he need not clean or wash.

Shach (11): One may clean or rinse the mouth first. The order does not matter.

Gra (9): The Rashba explains that it suffices to clean or rinse. If not, why did Beis Shamai and Beis Hillel and Agra mention only one?

Pischei Teshuvah (5): The Pri To'ar says that it is not enough to chew. He must swallow to be considered cleaning. In any case one should not spit out, due to wasting food.

Rema: Some are stringent even for meat after cheese. This is the custom. After hard cheese, we do not eat it even poultry, just like we do not eat cheese after meat. Some are lenient. It is good to be stringent.

Gra (11): The Zohar is stringent. We do not say that it is against the Gemara, for also they (Chachamim of the Gemara) used to be stringent.