That’s why I mentioned pizza bianca / white pizza - it doesn’t include passata or tomato sauce, but it’s still pizza.
Cheese being added to the pizza is a bit trickier, but I’m tempted to say that the Romans already did this; they were big fans of cheese, and the white stuff in the afresco looks a lot like sheep cheese for me. And, well, cheese melting over hot bread is kind of obvious. Plus there are claims that mozzarella itself backtracks to those times, although it was originally made with sheep milk.