A zillion years ago in another life and at a far younger age, I worked in a pizza joint that also served pizza burgers. Pretty good actually. It was a french bread bun with pizza sauce on both sides and grated mozzarella on one side and grated cheddar on the other. That was melted in the oven. A burger was cooked and placed between the buns and there you go a pizza burger!
O-M-G....what a bastardization! :-(