John Gill Commentary 1 Samuel 2:15

"Yea, before they burnt the fat, the priest`s servant came, and said to the man that sacrificed, Give flesh to roast for the priest; for he will not have boiled flesh of thee, but raw." — 1 Samuel 2:15 (ASV)

Also before they burnt the fat
Which belonged to the Lord, and was to be offered to him by fire, in the first place, as it ought to be; and the order of sacrificing required that he should have his part first before the priest or the owner: but so impious were the priests become, that

the priest's servant came, and said to the man that sacrificed ;
not to the priest that offered, but to the man that brought his sacrifice to be offered by the priest:

give flesh to roast for the priest ;
meaning, not what was his by law, as the breast and shoulder, though for these he ought to have stayed until the fat was offered to the Lord; but other parts of the peace offering, which he had no right unto, for roasting or boiling, and yet in an imperious manner demanded it by his servant:

for he will not have sodden flesh of thee, but raw
though this was not the only reason of this demand, because they liked roast meat better than boiled; but because the three forked flesh hook did not always bring up the best pieces out of the boiling pot; and therefore he resolved to have flesh raw, that he might have the best, as well as dress it to his own liking.