Preparations for the Seder
5. After the Beit Hamikdash (Temple) was destroyed (70 CE), the Sages ordained that two cooked foods should be placed on the table while the Haggadah is being recited, one to commemorate the "Korban Pesach" (1) and one to commemorate the "Korban Chaggigah" (2), which were offered [on Pesach] when the Beit Hamikdash was standing.
It is customary that one of these cooked dishes be meat. Generally, the foreleg ("zeroa" - commonly referred to as the "shankbone" (3)) of an animal is used, as an allusion to the outstretched ARM ("zeroa netuyah") with which G-d redeemed the Jewish people. It should be roasted directly over coals (or fire) to commemorate the Korban Pesach, which had to be "roasted by fire" (Exodus 12:9).
The second dish should be an egg, because the Aramaic term for egg is "be'ah", which also means to "want" or "desire." [Thus, the combination of the egg and the zeroa can be interpreted to mean]: "The Merciful One DESIRED to redeem us with an outstretched ARM." The egg may be cooked or roasted (4).
Both [the egg and the zeroa] should be cooked or roasted before the commencement of Yom Tov. If one forgot, or the fourteenth of Nissan fell on Shabbos, one may roast or cook them at night (after Yom Tov has begun) (5). One must, however, eat them on the first day of the festival. Similarly, on the second [Seder] night, one should roast or cook them at night, but one must eat them on the second day of the festival.
[The rationale for having to eat it on the same day (6) is that] it is forbidden to cook on one day of a festival in order to eat the food on the second day or on a weekday. The zeroa should be eaten during the day only, since it is forbidden to eat roasted meat on the [first] two nights [of Pesach] (7). Nevertheless, even if the zeroa and the egg were roasted before Yom Tov began, they should not be discarded afterwards. Rather, they should be placed in a dish that is cooked on the second day of Yom Tov, and eaten then.
(1) On the afternoon of the 14th of Nissan, the Pesach sacrifice, owned and prepared by each family or group of Jews, was offered in the Beit Hamikdash, and its meat was eaten that night, the first night of Pesach, at the Seder, along with matzah and marror.
(2) There was a Biblical obligation for every male to appear in the Beit Hamikdash on the first day of each of the three "Regalim" ("pilgrim festivals" - Pesach, Shavuos and Succos), and to bring a peace offering ("korban shelamim") called a "Korban Chaggigah." On the afternoon of the 14th of Nissan, it was customary to offer a Korban Shelamim along with the Korban Pesach, and to eat the meat that night at the Seder. This Korban Shelamim, offered on the 14th of Nissan, was called the "Chaggigas Arba'ah Asar."
(3) If one uses a bone, it should have some meat on it.
(4) The egg is a mourner's food. Therefore, another reason the egg is used, is as an expression of mourning over the destruction of the Beit Hamikdash, and our subsequent inability to offer the Korban Pesach. Also, Tisha B'Av (the day we mourn over the loss of the Beit Hamikdash) always occurs on the same day of the week as the first night of Pesach (Ramah 476:2).
(5) Cooking is permissible on Yom Tov.
(6) The Jewish "day" is from sunset to sunset.
(7) The reason for this custom, is so that one should not assume, in error, that he is eating the meat of the Korban Pesach. The custom includes not eating meat or poultry (or anything that requires ritual slaughter), whether roasted, barbecued or broiled over an open fire. Most authorities also prohibit eating pot roast (meat roasted in a pot without water). Meat which was roasted and then cooked is permissible (See Halachos of Pesach by Rav Shimon Eider, Chapt 24: K3).