An unneccessarily small blunt. Its made when a person empties the tobacco from the cigar to replace with weed but doesnt have nearly enough weed to refill the cigar before rerolling. Its basically a joint.

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

(n.) An unnecessarily small blunt.

A baby blunt is to a Blunt, as a pinner is to a Joint.