Alliteration is fun when you try to read it out loud quickly. You're sure to mix up and mess up the words, and that's funny. We have lots of tongue-twisters based on this principle.
Шла Саша по шоссе и сосала сушку.
На дворе трава, на траве дрова.
Шит колпак не по-колпаковски. Надо колпак переколпаковать, перевыколпаковать.
Try to say them quickly and you'll ...
This is a rhetorical device known as alliteration.
Бри means "brie", a type of French cheese. Брют means "brut", a type of champagne. These words are not funny in and of themselves, but they do make the alliteration work.
Being funny is a very subjective thing. This particular alliteration is not very funny to me personally, but I can see ...