I thought the Papa John's thing was their version of a quesadilla?
In their "Riddle" commercial -
https://www.ispot.tv/ad/ZW6C/papa-johns-papadias-riddle - they ask who should get credit, the inventor of pizza or the inventor of folding. A folded pizza is a calzone. I suppose one could argue that a quesadilla is basically a Mexican calzone.