Cuban sandwiches are made of pork, ham, mustard, pickles, and cheese on fluffy, crusty Cuban-style bread, while medianoches use a softer bread called "pan suave."
Containing all the same ingredients as a Cuban, the pan suave bread used for a medianoche is eggier and more sugary, adding richness and sweetness to the sandwich.
Medianoches are named after the time they are often eaten — midnight — since its bread is supposedly easier on the stomach for people who have been drinking and partying.
If you’re hoping to make the sandwich at home, you can use challah as a substitute for the bread, since it has a similar soft, eggy, enriched texture and flavor.