Cut rounds from pizza dough using a 2-inch round cutter to make tiny individual crusts. Place pizza rounds on a baking sheet, top with sauce, and cover with mozzarella. Sprinkle a light dusting of grated Pecorino or Parmigiano on top. Bake until cheese is perfectly melted, approximately 10 minutes.
Cut basil leaves into thin strips and sprinkle on top of pizzas with some more grated cheese before serving.