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.
A person who engages in Cleveland Browning; a person who hooks up with a Cleveland Brown, which is a girl with a nice body but an ugly face, also known as a bagger or butterface.
John is such a Cleveland Browner. For the third time this semester he bagged a bagger - he hooked up with yet another ugly chick who happened to have a nice body.