It should be pointed out that Brecht's use of the German word "fressen", instead of the usual word "essen," is not accidental and alludes to his low opinion of humanity as mere animals hidden under a thin veneer of culture and manners.
The German maxim "Tiere fressen, Mensche essen" (animals feed, humans eat) differentiates between the animal-like frenzy of eating and the human concept of eating, with table manners and conversation. My sense is that the germanic use of the word "fressen" is not like cows or sheep grazing on grassy hillsides, but connotes a predatory scene, like a lion hunting a gazelle, killing it, and then tearing it apart savagely for the meat.
Brecht's phrase is highly ironic. The reader expects to read the phrase, "Erst kommt das Essen, dann kommt die Moral." using the usual German word "essen" to mean, "first comes the meal, then comes the moral." Brecht's almost shocking use of the word "fressen" implies we are nothing more than animals, and our first priority is to be fed. Then to hear that Father will deliver a moral to us animals after the meal conjures up visions of a pride of lions sitting around the bones of some fresh kill, bloated and sated, while the alpha male pontificates about being polite to grandmothers, usw. It is a clever twist to what could be a very prosaic, pablum phrase. This, of course, is why Berthold Brecht is a genius.
User-contributed facts & anecdotes
"I don't think this is enough for its own write-up, but I thought I would mention to you that "fressen" is Yiddish slang for oral sex... or, often more specifically, cunnilingus. While Brecht himself was not a Jew, Kurt Weill was. Perhaps this is relevant, perhaps not." -- dharbigt
"my bf just did a production of Hansel und Gretel, where he mentioned the Witch's verb being "fressen" while the children's verb was "essen"" -- Sondheim
An alert NinjaPenguin has found a web site where you can buy tee shirts with this saying on it. Thanks NinjaP!