Exodus 23:18

"The first part of this verse has nothing to do with eating anything leavened. Rather it means that individual Israelites were not to kill the Passover lamb while leaven was still in their houses. The second half of the verse makes no reference to fat as such; but as the parallel verse in Exodus 34:25 b says, the ’sacrifice from the Passover Feast’ (here lit., ’sacrifice of my feast’) shall not ’remain until morning’ (cf. Exodus 12:10)." [Note: Kaiser, "Exodus," p. 445.]

The "fat" means "the best part," here the whole sacrifice.