I think that I'm on to something.
Took a pita bread from my favorite bakery. Very fluffy with an elastic, well gelatinised crumb. Filled it with fresh mozzarella, tomatoes and basil + some salt. Then heat it all up (covered in a moist towel) until the cheese melted. Served with some OO for dipping.
What I got was in a way closer to the "Neapolitan pizza ideal" than any pizza I've made. The interior crumb soaked the cheese and tomato juices and was reminiscent of a pizza's top layer. The pocket kept the cheese hot and prevented it from drying and solidifying.