Sefer HaChinuch ספר החינוך

The commandment of eating the remainders of the meal-offering: That the priests were commanded to eat the remainders of the meal-offerings — meaning to say after they separated from it that which they would offer on the altar, they would eat all the rest, as it is stated (Leviticus 6:9), “What is left of it shall be eaten by Aharon and his sons; as matsahs shall it be eaten, etc.” And the language of Sifra, Tzav 2:9 is, “‘As matsahs shall it be eaten’ is a commandment; ‘her levirate husband shall have sexual relations with her’ (Deuteronomy 25:5) is a commandment” — meaning to say that both of them are positive commandments, not optional.

I have written from the roots of the commandment above (Sefer HaChinukh 102) in the commandment of “They shall eat that with which atonement was done” in Ve’atah Tetsaveh — that it is an honor for the sacrifice that the actual servants of God, may He be blessed, eat it, and not that it be given to lesser ones to eat it, etc. as it is written there.

From the laws of the commandment is that which they, may their memory be blessed, said (Menachot 72b) that all of the meal-offerings that were offered on the altar were skimmed — and the skimming was completely incinerated on the altar, and the rest was eaten by the priests — except for the meal-offering of the males of the priesthood, which is not skimmed, as it is stated (Leviticus 6:16), “And every meal-offering of a priest shall be whole; it shall not be eaten.” It comes out that the inauguratory meal-offerings and the griddled ones, and a priest that brought a sinner’s meal-offering or a voluntary meal-offering — [all these offerings] were burnt on the altar and not skimmed. The meal-offering of a priestess (Sotah 23a) is skimmed and its remnants are eaten; as we say, it is specifically a priest [that is stated by the Torah], and not a priestess. And the rest of its details are elucidated in Menachot. (See Mishneh Torah, Laws of Sacrificial Procedure 10.)

And it is practiced at the time of the [Temple] by the males of the priesthood, as it is stated (Leviticus 6:11), “Every male of the Children of Aharon shall eat it.” [If] he transgressed and did not eat it, he has violated this positive commandment.