Fried Neapolitan Pizza is made from a potato based dough that is then deep fried and topped and baked with fresh tomatoes, basil, and parmesan cheese.
Heat the oil. Fill a heavy bottomed frying pot with about 4 inches of vegetable or canola oil. Heat the oil over medium heat until it reaches 350 degrees.
Make the dough. Bring a large pot of water to a boil. Add the diced potatoes to the boiling water and cook until a fork can easily pierce them, about 5-10 minutes. Mash the potatoes with a fork or a potato masher until there are no chunks. In a large bowl or stand mixer, combine the potatoes, flour, eggs, egg yolks, 3 tbsp of parmesan cheese, and sugar. Mix the dough until it comes together. The dough will be very sticky.
Shape the dough. Pour and scatter about 1 cup of flour onto your work surface. Flour your hands. Dump the pizza dough onto the floured work surface and divide the dough into 8 small balls. Use your hands to flatten the dough into 5 inch discs. Use more flour if needed.
Deep fry the pizza. Place one pizza disc in the frying oil at a time. Deep fry on each side for 3-5 minutes, until they are golden brown. Remove the pizza discs and place them on a paper towel lined plate.
Sauté the "sauce". In a small pan, heat a splash of olive oil over medium heat. Add the tomatoes and basil, then a dash of salt. Sauté the tomato mixture until they are slightly softened, about 2-3 minutes.
Bake the pizzas. Lay the pizza discs on a baking sheet. Spoon 3-4 tablespoons of the tomato mixture on to the top of the pizzas, then sprinkle with the remaining parmesan cheese. Bake the pizzas for 10 minutes, then slice and serve. Mangia!