Make sure the shrimp has been gently cut through the back and deveined. Lay a piece of plastic wrap on a sturdy counter or cutting board. Lay the sliced shrimp flat on the plastic wrap and fold the other half of the wrap over the top. Gently pound the shrimp with a meat tenderizer or mallet or the side of a clever or a reasonably heavy can until it is flattened. Repeat with the other 3 shrimp.
Place the flour, beaten egg, and crumbs in three separate containers. Season the pounded shrimp with salt and pepper. Dredge the seasoned shrimp carefully in the flour, eggs, and crumbs and place on a tray with waxed or parchment paper. Heat a skillet over medium flame for 1-2 minutes. Add the olive oil. Heat the oil for 20-30 seconds. Add the breaded shrimp and slightly reduce the flame. Cook to a golden brown on each side, turn off the heat, and remove the shrimp to a platter with paper towels, about 6 minutes.
Pre-heat the oven to 450 degrees. Place the shrimp evenly on a baking sheet. Spoon a bit of sauce on each, or to your taste. Sprinkle the sauced shrimp with grated Parmigiano and then the mozzarella. Bake the shrimp in the pre-heated oven for 8 minutes until you like the color of the cheese. Remove the baked shrimp from the oven, place each on a plate, and sprinkle with a bit more grated cheese.