When feeling ill and preparing breakfast, usually after a night of heavy drinking, one vomits into the pan in which they are cooking. Thus, a vomelette is created.
Note: Eggs do not necessarily have to be the food being prepared.
Joe: Dude, I was so hungover from last night, that I made a vomelette this morning.
Frank: Oh god! What did you do with it?
Joe: Well, I still ate it. Eggs are expensive.