1. Heat oven to 350°F .
2. Set out 2 dishes. In one dish, whisk together the eggs, milk, and salt. In the other dish, mix the bread crumbs with the Parmesan and mozzarella. Coat the chicken in the egg mixture. Gently shake off the excess egg, then transfer to the bread crumb mixture. Coat the chicken evenly on both sides, pressing the breading to adhere. Set on a baking sheet and repeat with remaining chicken.
3. In a large skillet, heat 2 tablespoons of olive oil over medium heat. Set a baking sheet with a wire rack on top nearby. Add 2-3 pieces of chicken to the hot oil, being careful not to overcrowd the pan. Cook until golden brown on both sides, flipping once, about 5 minutes total. Transfer the cooked chicken on the wire rack to drain. Add more olive oil as needed, and repeat with remaining chicken.
4. Spread a thin layer of marinara sauce in the bottom of a 9×13-inch (22 x 33 cm) baking dish. Arrange half of the chicken in a single layer over the sauce and top with half of the mozzarella. Add another layer of sauce and top with the remaining chicken, followed by the remaining mozzarella. Finish with a layer of sauce and top with the Parmesan.
5. Bake until the chicken reads 165°F, 30-40 minutes. Let sit for a few minutes before serving.