I don’t think so, not at a regular pizza restaurant. I used to work at a pizza restaurant, and it would not be feasible to cook those ingredients in a pizza oven, because it would wreck the surface of the oven.
On the other hand, if you wanted something similar, you might be able to request that at a more traditional Italian restaurant, because they could put the ingredients in a skillet or stoneware dish and then either cook it on the stove, or put the stoneware plate/bowl into the oven and kind of bake it.
I have had something similar in Mexican restaurants with a dish called Rajas Poblanos. They take strips of poblano chili peppers, mix in some Mexican cheese, such as Queso Blanco, or Queso Fresco, then they put it in a stoneware dish and put cook that under the broiler. You could probably do that at home, too with your mozzarella cheese and other toppings. You could also simply put the ingredients in a bowl and put it in the microwave, although you won’t get that crispy finish on top.