Use Pasta as Dough
You hereby have permission to overcook your pasta. Chef Davide Scabin of Combal.Zero in Rivoli, Italy, and New York City's Mulino a Vino cooks his pasta well past a chewy al dente, then purées it and turns it back into dough. He uses it for dishes like giant stuffed ravioli; macaroni soufflé, in which the purée subs for the flour and butter; and fried bomboloni.
Cook pasta until mushy. Let cool; drain. Add salt and purée in a food processor or mix by hand until it forms a sticky dough.
Divide dough in half; flatten between sheets of greased parchment paper and chill. Roll dough until ⅙″ thick.
Cut out circles with a round cutter. Place 1 slice mozzarella and 2 tbsp. filling over each circle; fold in half and pinch edges.