Zevachim 90 - Eating the Old Meat First

More special actions precede the less specials ones ; thus, even though normally a sin-offering comes before a guilt-offering, a guilt-offering of a metzora (spiritual leper) comes before his sin-offering, because it prepares him for further purification. Just as they precede in offering, so they precede in consumption.

If we have a peace offering from yesterday and a sin-offering from today, then the peace offering should be eaten first, because it would an expression of disdain to allow yesterday's offerings to spoil - this is the opinion of Rabbi Meir, but the Sages maintain that the regular rule of "more sacred comes first" still applies even here.

For consumption, the Kohanim are allowed to cook the offerings in any way they like, to roast, boil, or fry them, and to add any spices.

Which comes first, more frequent or more sacred? Let's prove it from the additional Shabbat offering itself: it is more sacred, and nevertheless the more frequent daily offerings comes before it! - No, that is no proof, because  on Shabbat  the daily offering is also more special. After making five more attempts to find a proof, the Talmud leaves this unresolved.

Jean Baptiste Simeon Chardin - A "Lean Diet" with Cooking Utensils