Move the oven rack to the upper center position. Turn the broiler to high and let it fully preheat.
In a shallow bowl, mix flour, Parmesan, salt, pepper, paprika, and garlic powder.
Cut each chicken breast into 3 pieces. Place between two sheets of plastic wrap and pound to about 1/4-inch thick. Rub both sides with 1 tablespoon olive oil total. Coat each piece evenly in the flour mixture.
Heat 2 tablespoons olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Once butter is melted, add half the chicken and cook 3-4 minutes on the first side until golden. Flip and cook 1-2 minutes more. Transfer to a cooling rack and sprinkle lightly with salt. Repeat with remaining chicken, wiping out the pan and adding more oil and butter as needed.
Meanwhile, prepare the cheesy topping. For each serving, spoon about 3/4 cup marinara into a small oven safe pan. Sprinkle 3 tablespoons mozzarella evenly in the center and finish with a light sprinkle of Parmesan. Broil for 2-4 minutes, watching closely, until melted and deeply golden.
Divide cooked chicken pieces evenly among 3 plates. Working carefully and quickly, tilt the hot pan so the sauce and bubbly cheese slide over the chicken on a plate. Repeat for remaining servings and serve immediately.
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Notes
Note 1: Use fresh grated Parmesan, not shelf stable (that's not real cheese!), for the best flavor and crisp texture.Note 2: You can use the same Parmesan for both the chicken and the cheesy topping if you prefer, but I love using a block of Parmesan and grating it with a microplane over the mozzarella. It's SO GOOD.Storage: This recipe is best enjoyed fresh since the chicken softens as it sits. If planning for leftovers, store the pounded, uncooked chicken separately from the breading and sauce. Bread and pan fry the chicken fresh before serving, and prepare the cheesy topping right before eating.