Gemara

15b - Mishnah - Beis Shamai: One must make two Tavshilim for Eruv Techumim;

Beis Hillel say, one Tavshil suffices.

16a - Abaye: The Mishnah says that one makes a cooked food from before Yom Tov. Bread is not valid.

Question: What is the reason?

Version #1 - Suggestion: We require an accompaniment (for bread, to show that it was prepared for Shabbos).

Rejection: Porridge is not an accompaniment, yet Abaye taught that it is valid!

R. Zeira derided Benei Bavel, for they eat bread with (porridge, which is made from grain just like) bread.

Answer: We require something uncommon. Bread is common, and porridge is not common.

Version #2 - Suggestion: We require something uncommon. Bread is common.

Rejection: Porridge is not common, yet Abaye taught that it is invalid!

Answer: We require an accompaniment. Bread is not an accompaniment, and neither is porridge.

R. Chiya - Beraisa: One may rely on lentils in the bottom of the pot, as long as there is a k'Zayis.

R. Yitzchak brei d'Rav Yehudah: One may scrape fat off a knife and rely on it if it is a k'Zayis.

16b - R. Aba: Eruv Tavshilin requires a k'Zayis, whether it is for one person or 100.

Mishnah: If he ate the Eruv or lost it, he may not rely on it to cook expressly for Shabbos. If any of it remained, it is permitted.

Suggestion: 'Any of it' means even less than a k'Zayis!

Rejection: No, it means a k'Zayis.

Question - Beraisa: The Tavshil may be roasted, or even pickled, overcooked, cooked, or Kulyas ha'Ispanin (a kind of tuna) on which hot water was put from before Yom Tov. There is no Shi'ur to Eruv Tavshilin at the beginning or the end.

Suggestion: There is no Shi'ur at all!

Answer: No, there is no upper Shi'ur, but there is a lower Shi'ur.

Rishonim

Rif and Rosh (2:5): We require an accompaniment. Therefore, bread and porridge are not valid. One may use lentils in the bottom of the pot, or fat scraped off a knife, if there is a k'Zayis The Tavshil may be roasted, or even pickled, overcooked or cooked, or Kulyas ha'Ispanin rinsed in hot water from before Yom Tov. Eruv Tavshilin requires a k'Zayis, whether it is for one person or 100.

Ran (DH Amar): Even though the lentils were left unintentionally, we do not say that they are unimportant and Batel. Kulyas ha'Ispanin is salted and eaten raw; rinsing it in hot water is its cooking.

Ran (10a DH Amar): R. Tam says that Beis Shamai and Beis Hillel argue about whether or not two Tavshilim are needed to roast and cook. Beis Shamai require two. Even though both are cooked, it is a reminder of two kinds of cooking. Beis Hillel say that one Tavshil permits roasting and cooking.

Rambam (Hilchos Yom Tov 6:3): The Shi'ur for Eruv Tavshilin is at least a k'Zayis, whether it is for one person or 1000. One may not use bread or grits or similar things for Eruv Tavshilin. A Tavshil used to accompany bread is required, such as meat, fish, eggs or similar things. One may even rely on lentils in the bottom of the pot, or fat scraped off a knife, if there is a k'Zayis.

Magid Mishnah: Produce is not valid.

Rambam (4): The Tavshil may even be roasted, pickled, overcooked or smoked. Even small fish rinsed in hot water may be used, for rinsing them is their cooking.

Magid Mishnah: The Yerushalmi allows smoked food.

Poskim

Shulchan Aruch (OC 527:3): The Shi'ur for the Tavshil is a k'Zayis, whether it is for one person or 1000, both at the beginning and at the end.

Mishnah Berurah (8): One should use a full loaf and an important piece of fish or meat for Hidur Mitzvah.

Kaf ha'Chayim (21): It is a disgrace to use for the Mitzvah bread and a Tavshil that are substandard and are prone to be thrown out. It is good to use hardboiled eggs and well roasted meat, for these do not spoil within two days even in hot climates.

Rema: Some require a k'Beitzah of bread and a k'Zayis of a Tavshil. L'Chatchilah one should do so.

Beis Yosef (DH Kosav ha'Mordechai): The Mordechai cites this from the Yerushalmi. This is unlike the Bavli, which says that the Shi'ur is a k'Zayis and does not distinguish bread from a Tavshil.

Mishnah Berurah (11): The Maharil would use the Eruv loaf for Lechem Mishneh for the evening and morning Shabbos meals, and cut it at Seudah Shelishis. Since it was used for a Mitzvah, it is proper to use it for another Mitzvah.

Shulchan Aruch (4): The Tavshil must be fitting to accompany bread. This excludes porridge.

Magen Avraham (2): Even where people use it to accompany bread, their practice is Batel to the universal practice. If an accompaniment (in most places) is not eaten with bread in a certain place, it is invalid for Eruv Tavshilin there. Rashi requires something not eaten every day, so it will be evident that it was prepared for Shabbos.

Shulchan Aruch (5): The Tavshil may even be roasted, overcooked, pickled or smoked.

Beis Yosef (DH v'Da): The Tur omitted pickled, even though a Beraisa permits it. Perhaps he concluded that this is not the Halachah, because salted fish are considered pickled, yet they may not be used. The Halachah follows the Poskim that allow pickled food.

Magen Avraham (3): Pickled or smoked foods are valid only if they are fitting to eat that way. Salted foods are invalid even if they are fitting to eat that way.

Mishnah Berurah (13): Even though salted herring is fitting to eat raw, it is invalid. However, if it was at the bottom of the barrel it is pickled, so it is valid.

Even small fish rinsed in hot water may be used if rinsing them is their 'cooking' to prepare them to be eaten. One may rely on cooked apples (Rema - or other cooked fruits) and on small cooked fish.

Source (Beis Yosef DH Garsinan): The Yerushalmi allows even cooked foods which could be eaten raw.

Magen Avraham (4): It appears that the Magid Mishnah does not allow cooked fruits (unless they are normally used for accompaniment). He would not need to teach that raw fruits are invalid!

Mishnah Berurah (17): Kulyas ha'Ispanin are soft, so rinsing it in hot water suffices to cook it.

One may even rely on lentils in the bottom of the pot, or fat scraped off a knife, if there is a k'Zayis.

Mordechai (673): There is an argument in the Yerushalmi about whether or not he must stipulate before Yom Tov (that he will rely on them for the Eruv if he forgets to make Eruv Tavshilin). Rashi and the Ri require him to stipulate before Yom Tov. L'Chatchilah one should prepare a Tavshil; b'Di'eved, he may rely on this. Some say that if he did not, b'Di'eved he may stipulate on Yom Tov. Since this is mid'Rabanan, we follow this opinion.

Beis Yosef (DH Kosav ha'Mordechai Piresh): Even b'Di'eved one should not be lenient to stipulate on Yom Tov. The Mordechai holds that even from before Yom Tov one should not rely on the lentils or fat. It seems that if he has nothing else he may do so l'Chatchilah.

Taz (7): The Mordechai also permits this if he has nothing else, for this is like b'Di'eved. All agree that the ideal Mitzvah is to prepare a proper Tavshil. The Maharshal says that stipulation is needed only for things like lentils and fat. If one made a Tavshil for the sake of Eruv Tavshilin and forgot to stipulate and bless, he may rely on it b'Di'eved.

Mishnah Berurah (20): If one made a Tavshil of lentils one may use it l'Chatchilah like anything else, as long as it is an accompaniment in that place.