We are up to Mishnah 7 in the tenth chapter of tractate Zevachim, where we conclude the topic we have been discussing - the ways in which the sacrifices are eaten.
"Uvechulan hakohanim rasha'in leshanot ba'achilatan, le'ochlan tzluyim shelukim umevushalim":
"Uvechulan" - With all of the eaten sacrifices enumerated in the Mishnah.
"Hakohanim rasha'in leshanot ba'achilatan" - They have permission to change the way the meat is prepared for eating.
"Tzluyim" - Roasted over a fire; "shelukim" - thoroughly cooked in a sauce, like a stew; "umevushalim" - like a pot roast. They are permitted to do as they please.
The Reason for the Permission - "Lecha netatim lemoshchah":
The novelty of the Mishnah is based on the verse in Numbers chapter 18: "Lecha netatim lemoshchah" ("I have given them to you for a portion of greatness") - the sacrifices were given to the kohanim so that they may enjoy them in a royal manner. Just as royalty eat their food in whatever form they desire and do as they please, so too the kohanim eat the sacrifices in the manner most pleasing to them.
It is worth noting that this applies equally to an Israelite: a person who is not a kohen, who brings his peace-offerings, eats them in the manner that he finds most enjoyable and tasty. The novelty here is that even the kohanim, and even when it comes to the most holy sacrifices, are permitted to eat them in any way they desire.
Roasted with Mustard - A Question from the Gemara:
The Gemara in Chullin 132b explains that the manner in which the kohanim must eat the meat is specifically roasted with mustard, which seemingly contradicts the permission to vary it found here. However, it can be said that this is the default option: all things being equal, the most "objective" and royal way to eat the sacrifices is meat roasted with mustard, which is the tastiest method. But if a kohen's appetite is drawn to a different method, he is certainly permitted to vary it - and certainly so when he eats the exact same food every evening for the entire week.
As Tosafos points out, this is the meaning of the words "leshanot ba'achilatan": to change from the regular way of eating. Ideally, when a person has no special preference, the Torah teaches that the choicest way to cook the meat is roasted with mustard; but permission is given to vary, and it is logical that a kohen who eats from the sacrifices every night would desire variety.
Spices in the Meat of the Sacrifices:
The Mishnah adds: "Velatet letochan tavlei chullin vetavlei Terumah" - It is permitted to add spices, such as pepper, to flavor the meat according to his desire. There are two novelties in this:
Tavlei chullin - Even though it is forbidden to bring non-sacred items (chullin) into the Temple courtyard, for the purpose of eating the meat of the sacrifices, it is permitted to bring in spices that are not sanctified.
Tavlei Terumah - A spice that comes from Terumah produce, such as Terumah pepper or Terumah olive oil, is also permitted.
Rabbi Shimon permits this, because a person has the right to act as he wishes. However, this requires some analysis: Kodashim have a limited time window in which they are permitted to be eaten - the rest of the day, or until the next day, depending on the type of offering - a day or two at most. In contrast, Terumah has no deadline for being eaten, and there is even a separate mitzvah to protect Terumah from being ruined, as the verse states regarding it, "the safeguard of My Terumah." When a person mixes Terumah spices into kodashim meat, if he waits beyond the time frame for eating the meat, he will be forced to destroy the meat, and the Terumah will be destroyed along with it. The question, then, is whether it is permitted to put Terumah at risk, and Rabbi Shimon says that there is no problem with doing so.
This is indeed Rabbi Shimon's consistent approach. As we may recall, in chapter 8, mishnah 3, it says that if two animals became mixed up, one an asham and one a shelamim, Rabbi Shimon holds that this is not a concern, but rather one should treat both of them with the stringencies of an asham. The problem there was that by doing this he is shortening the time frame for eating the meat, since the shelamim is eaten for two days and the asham for only one day - and nevertheless, he ruled that there is no prohibition against this.
However, this is not the halachah, and here Rabbi Meir appears once again: "Rabbi Meir omer, lo yiten letocho tavlei Terumah" - he should not put Terumah into the kodashim meat to spice it, "shelo yavi et haTerumah lidei f'sul" - since by doing so he increases the possibility that the Terumah will have to be burned if the meat is left over beyond its time limit, and once it becomes notar it must be burned. Therefore, initially one should not put any Terumah in it at all.
In summary: The halachah is that it is permitted to add chullin spices, but one may not add Terumah spices, so that the Terumah will not come to a state of disqualification and require destruction.