 It is so named because of the sandwich's popularity as a staple served in Havana's night clubs right around or after midnight.A "medianoche" consists of roast pork, ham, mustard, Swiss cheese, and sweet pickles.It is a close cousin to the Cuban sandwich, the chief difference being that a "medianoche" is made on soft, sweet egg dough bread similar to Challah rather than on crustier Cuban bread.