Gemara

46b (Rav Chisda): If one bakes on Yom Tov for the sake of a weekday, he is lashed;

He does not exempt Ho'il (since) if guests would come he could serve the food to them [so it turns out that he cooked for consumption on Yom Tov].

(Rabah): He is not lashed, due to Ho'il.

Question (Rabah, against Rav Chisda): You do not say Ho'il. How may we cook on Yom Tov for Shabbos [when Yom Tov is on Erev Shabbos]?

Answer (Rav Chisda): It is permitted through Eruv Tavshilin. (One begins preparing for Shabbos before Yom Tov, and may prepare more on Yom Tov.)

Question (Rabah): Eruv Tavshilin (mid'Rabanan) cannot permit an Isur Torah!

Answer (Rav Chisda): Mid'Oraisa, one may cook on Yom Tov for Shabbos. Chachamim decreed, lest people come to cook on Yom Tov for the sake of a weekday;

Chachamim required Eruv Tavshilin to remind people that one may not cook freely on Yom Tov for the sake of other days.

Question (Mishnah): [Baking] Lechem ha'Panim does not override Shabbos or Yom Tov.

If [mid'Oraisa] one may cook on Yom Tov for Shabbos, they should override Yom Tov!

Answer: Chachamim permitted a near Shevus [for Shabbos that is right after Yom Tov, through Eruv Tavshilin], but not a far Shevus [for the following Shabbos].

Beitzah 15b (Mishnah): On Yom Tov that is Erev Shabbos, one may not cook expressly for Shabbos. One may cook for Yom Tov, and if there are leftovers he may have them on Shabbos. One makes a Tavshil from before Yom Tov and relies on it for Shabbos.

Beitzah 17a (Beraisa): One may not bake on Yom Tov Rishon for Yom Tov Sheni. We have a tradition that a woman may fill the pot with meat [and cook it on the first day] even though she needs only one piece [today]. A baker may fill a barrel with water [and heat it] even though he needs only one flask. However, he may bake only what he needs;

R. Shimon ben Elazar says, she may fill the entire oven with bread, for it bakes better when the oven is full.

(Rava): The Halachah follows R. Shimon ben Elazar.

Rishonim

Rambam (Hilchos Yom Tov 1:9): One may not bake or cook on Yom Tov what he will eat during the week. Melachah for the sake of food is permitted only for what he will eat that day of Yom Tov. If one made food for Yom Tov, and there was left over, he ay eat it on a weekday.

Rambam (10): A woman may fill a pot of meat even though she needs only one piece. A baker may fill a barrel with water, even though he needs only one flask. A woman may fill the entire oven with bread, even though she needs only one loaf, for it bakes better when the oven is full.

Rambam (11): One who cooks or bakes on Yom Tov to eat that day, or he invited guests and they did not come, he may eat the remainder on a weekday or Shabbos, as long as he does not scheme. If he schemed it is forbidden, even on Shabbos after Yom Tov. Chachamim were more stringent than about scheming than about Mezid.

Poskim

Shulchan Aruch (503:1): One may not bake, cook or slaughter on Yom Tov for the sake of the next day, even if the next day is Shabbos or Yom Tov, even if it is the second day of Rosh Hashanah.

Source (Beis Yosef DH Asur): We learn from Beitzah 17b. All the more so one may not cook on Yom Tov for Chol. One may not cook on Yom Tov Rishon for Yom Tov Sheni, for perhaps the second day is really Chol. This applies even to Rosh Hashanah. We consider them to be one Kedushah to be stringent, but not to be lenient. Further, nowadays (the calendar is fixed, so always) the first day is the primary Kedushah.

Bi'ur Halachah (DH b'Yom): Surely one may not begin a Melachah of food during the day if he would not be able to benefit from it before Shki'ah.

Kaf ha'Chayim (5): Sho'el u'Meshiv (2, 2:10) permits to cook Bein ha'Shemashos of Yom Tov Rishon of Galus for the sake of minors.

Bi'ur Halachah (DH v'Afilu): The Gra connotes that the Rambam and those with him permit for the sake of the second day of Rosh Hashanah. The first day is Vadai Yom Tov mid'Oraisa! Perhaps he holds that due to Ho'il, the Torah permits cooking even for a weekday. Since both days are one Kedushah, Chachamim permitted for the second day. Even according to this, the food must be ready to benefit from during the day, in order to say Ho'il.

Shulchan Aruch (ibid.): However, a woman may fill a pot of meat even though she needs only one piece.

Beis Yosef (DH Aval): Rashi explains that it is permitted to cook or bake extra because it is one exertion. The Rashba permits because the person wants to eat a fatter piece. The Rashba would permit to add additional pieces to a pot, but Rashi would forbid. We can be lenient because this is a mid'Rabanan matter. The Rashba agrees that one may put extra water on the fire only in one exertion, i.e. the pot is already full, because the water is no better when a full pot is cooked.

Mishnah Berurah (6): Even if she intends for the night, which is Chol, it is permitted, since he needs a piece for Yom Tov. Many Acharonim say that she may not say that she cooks for the night. B'Di'eved, this does not forbid.

Mishnah Berurah (7): Even if she needs only [the rest of] the Tavshil (cooked food) or only the gravy, it is permitted, for extra meat improves it. If one does not need to eat today at all, and he cooks primarily for the night, and he eats a little to avoid the Isur [of cooking just for the night], some forbid, for this is a scheme. Some permit, for in any case he eats some today. Also, it is before he ate [today]. The custom is to be lenient and cook in the morning for the sake of the night, and he tastes a little. We do not protest. This is for the sake of Yom Tov Sheni. One must be careful not to do so for the sake of Chol. One who is stringent like the first opinion, to only add to the pot needed for the morning meal, will be blessed.

Bi'ur Halachah (DH Aval): If the pot is already on the fire, it is permitted only if she intends that the added meat will improve the taste.

Kaf ha'Chayim (12): Even if the food is in a small pot, one may not put it in a big pot, since he intends to make it fattier.

Rema: All the more so one may slaughter even though he needs only a k'Zayis. Likewise, one may cook many pots and eat a bit from each.

Beis Yosef (ibid. and DH v'Yesh): SMaK (and Kol Bo) permit one to slaughter even if he needs only a k'Zayis, since there is no alternative. Semak forbids to bake or cook for the sake of Yom Tov Sheni even if he will eat a bit, for the above reasoning does not apply. This is difficult. One may cook a full pot of meat or bake a full oven of bread even though he needs only one piece or loaf (17a). Perhaps SMaK discusses our ovens. (Filling the oven does not improve the bread.) However, this does not explain why they forbid cooking extra. Perhaps they discuss after the person ate. Even so, Shechitah is permitted. The Gemara permits to slaughter a sick animal if he will eat a k'Zayis, even if he already ate. Semak holds that the same applies to a healthy animal.

Kaf ha'Chayim (18): It is permitted only if he can roast a k'Zayis before the time of his meal.

Kaf ha'Chayim (21): A Ba'al Nefesh should be stringent and cook only if he wants it for Yom Tov, but not if he intends to eat merely to avoid the Isur.

Shulchan Aruch (ibid.): This is only before he ate (his daytime meal). After eating he cannot say that he will cook and eat a k'Zayis, for this is a scheme. If he transgressed and cooked (or slaughtered), it is permitted.

Mishnah Berurah (12): All forbid after he ate the morning meal, for then it is an evident scheme.

Mishnah Berurah (13): Some say that this refers to the beginning of the Sa'if, cooking b'Mezid for Yom Tov Sheni. Perhaps we forbid one who schemed even b'Di'eved. Some say that it refers to scheming. This is more lenient than Mezid, for he ate some of it during the day.

Bi'ur Halachah (DH Mihu): The Magen Avraham says that if one schemed, it is permitted. He equates this to Mezid. This is more lenient than other schemes, for he ate from the food on Yom Tov. Really, it is not clear that even Mezid is permitted if he has other food!

Kaf ha'Chayim (22): If he intended to eat before his morning meal, even if he did not eat during the day, it is permitted.

Kaf ha'Chayim (23): If one ate a small meal, and intends to eat again in the afternoon, it is as if he did not yet eat.