Why isn't Chicken Parmigiana Kosher?

In three different passages the law לא תבשל גדי is written: once for the purpose of prohibiting the eating of meat-food with milk-food, once to prohibit us from deriving any other benefit (besides eating) from such mixture, and once to prohibit the boiling of meat with milk (Mekhilta d'Rabbi Yishmael 23.19.2; Chullin 115b).

(1) Every kind of flesh is forbidden to be cooked in milk, except for the flesh of fish and of locusts. And it is also forbidden to place it upon the table with cheese, except for the flesh of fish and of locusts. One who vows not to eat meat, he is allowed to eat the flesh of fish and locusts. Fowl may be placed upon the table together with cheese but may not be eaten with it, the words of Bet Shammai. Bet Hillel say: it may neither be placed [upon the table together with cheese] nor eaten with it. Rabbi Yose said: this is one of the leniencies of Bet shammai and the stringencies of Bet Hillel . Concerning what table did they speak? Concerning the table upon which one eats; but on the table whereon the food is set out one may place the one beside the other, and not be concerned.

(4) It is forbidden to cook the meat of a clean animal in the milk of a clean animal or to derive any benefit from it. But it is permitted to cook the meat of a clean animal in the milk of an unclean animal or the meat of an unclean animal in the milk of a clean animal and to derive benefit from it. Rabbi Akiva says: wild animals and fowls are not included in the prohibition of the Torah, for it is written three times, “You shall not seethe a kid in its mother's milk;” to exclude wild animals, fowl, and unclean animals. Rabbi Yose the Galilean says, it is said, “You shall not eat any nevelah” and [in the same verse] it says, “You shall not seethe a kid in its mother's milk” (Deuteronomy 14:21) anything that is prohibited because of nevelah it is forbidden to cook in milk. Fowl which is prohibited because of nevelah, it might also be forbidden to cook in milk, Scripture says, “In its mother’s milk;” this excludes fowl which has no mother's milk.

The baraita adds: In the locale of Rabbi Yosei HaGelili they would eat bird meat cooked in milk. Evidently, Rabbi Yosei HaGelili maintains that the prohibition of meat cooked in milk does not include birds. The Gemara relates: Levi happened to come to the house of Yosef the bird hunter [rishba]. They served him the head of a peacock [tayvasa] in milk and he did not say anything to them. When Levi came before Rabbi Yehuda HaNasi, Rabbi Yehuda HaNasi said to him: Why did you not excommunicate these people who eat bird meat cooked in milk, contrary to the decree of the Sages? Levi said to him: It was in the locale of Rabbi Yehuda ben Beteira, and I said: Perhaps he taught them that the halakha is in accordance with the opinion of Rabbi Yosei HaGelili, who said that the phrase “in its mother’s milk” serves to exclude a bird, which does not have mother’s milk. If so, I could not prohibit it to them, and I certainly could not excommunicate them for following their ruling.

§ The Gemara continues discussing the consumption of poultry cooked in milk. The Sage Agra, the father-in-law of Rabbi Abba, taught: The meat of birds and cheese may be eaten freely [apikoren], i.e., there is no need to be strict in this matter. The Gemara notes: He, Agra, teaches it and he says it, i.e., explains his statement: The meat of birds and cheese may be eaten without washing one’s hands and without wiping the mouth between the consumption of each. The Gemara relates: Rav Yitzḥak, son of Rav Mesharshiyya, happened to come to the house of Rav Ashi. They brought him cheese, and he ate it. Next they brought him meat, and he ate it without first washing his hands. The members of Rav Ashi’s household said to him: But didn’t Agra, the father-in-law of Rabbi Abba, teach only that the meat of birds and cheese may be eaten freely? One can infer that with regard to the meat of birds and cheese, yes, one may eat them without washing one’s hands in between, but with regard to the meat of domesticated animals and cheese, no, one may not.

(4) So too, the meat of beast or bird cooked with the milk of beasts or cattle is biblically not prohibited from eating; hence, it is permissible to cook it and to derive a benefit from it. It is, however, prohibited from eating it on rabbinic grounds, so that the people may not reach out beyond what is permitted and transgress the biblical meat-milk prohibition by eating the meat of a clean animal with the milk of a clean animal, since the literal meaning of the verse is restricted to a kid in its mother's milk only. For this reason, the sages have prohibited all meat with milk.

(3) The law only applies with meat from a pure [kosher] animal and milk from a pure animal, but meat of a pure animal in milk that is impure, or meat from an impure animal in pure milk, is permitted to cook and benefit from. Meat of a wild animal and of fowl, even in milk which is pure, is permitted to cook and benefit from; and even eating is only prohibited rabbinically. Fish and grasshoppers are not prohibited [with milk] even rabbinically. RAMA: We make milk from almonds and place bird meat in it, since [milk and bird meat] is only rabbinically [forbidden]. But with meat from a domesticated animal, place almonds next to the milk, so that people don't misunderstand. This is as we said above, in chapter 66.