Place each halved chicken breast between two sheets of plastic wrap and pound with a meat mallet or rolling pin until each cutlet is 1/4–1/3 inch thick; set aside on a plate.
Season the flour with salt and pepper in a shallow bowl or baking pan and set aside.
In a second shallow bowl, whisk the eggs with a pinch of salt and pepper until combined.
Place the bread crumbs in a third shallow bowl and season with salt and pepper; mix to combine.
Dredge each pounded cutlet in the seasoned flour, shake off excess, dip into the beaten eggs, then press into the bread crumbs to coat completely; repeat for all cutlets.
Heat 1/2 to 3/4 cup olive oil in a large frying pan over medium-low heat. Fry the breaded cutlets 1–2 at a time for 2 1/2 to 3 minutes per side, or until golden brown, then transfer to a parchment-lined baking sheet.
Spoon about 1/4 cup pomodoro sauce (adjust to cover) evenly over each fried cutlet, then top with sliced mozzarella, shredded fontina, and a sprinkle of grated Parmesan.
Bake the prepared cutlets in a 450°F oven for 20–25 minutes, or until the cheeses are melted and lightly browned.
Remove from the oven, garnish with fresh chiffonade basil, and serve.