French toast

Brioche already has egg and milk and butter in it and now it has more. It is doubly fortified with those things now by an additional loose mixture of those same elements now with sugar and vanilla, and being a bit dry the bread soaks it up eventually. It does take some time. The absorption is not immediate. The bread must be saturated to nearly falling apart, barely capable of holding its shape, extremely wet like a filled sponge, and not merely coated with egg. If the bread is sufficiently dry to start out and the egg mixture sufficiently loosened then the bread will puff up while it cooks.