What is the Cuban Sandwich cigar? Great question…. A cuban sandwich cigar is a combination of long and short filler. All premium cigars are made with long fillers, (ie whole leafs) that run the length of the cigar. Sandwich rolls use one long leaf with short filler (ie pieces of tobacco) using the remnents from the premium cigars. What you get is a very economical cigar made from the same leaf as the premium lines.