The act of hooking up with a Cleveland Brown; banging a girl who is ugly but has a nice body; getting with a butterface; shagging a bagger.

when you're hungover as shit after a spending a night drunk as a skunk

This is when you end up buying some Cleveland Brown. This
happens when somebody you trust got fucked over and ended up
buying some bogus weed. You get a sample of some good shit,
and it only happens when you are in a hurry, such as going away on a trip ,or entertaining some new clients from out of town. You trust them and have a good buzz going, so you don't check it real well before you leave. When you get to your far off destination or after the club you burn one and all you get is a headache. Your new friends are laughing at you, thinking you are some kind of a dumb fuck. Or you are someplace where you have no connections or it could be a big problem trying to score.

When you get back to the shithead, they will try to make
it up by refunding your cash, but by then the damage has already been done.

Based on the scene from Family Guy where Cleveland Brown falls from a tub off a broken house after "Peter's shenanigans", Cleveland Brown-ing is just that.