Preheat the oven to 350°F and butter a 9x13-inch baking dish.
Combine the Ritz crackers, Parmesan and pepper in the bowl of a food processor. Process until the mixture forms fine crumbs, about 20 seconds.
Place the flour in a large bowl for dipping. Beat the eggs with the milk in separate large bowl until frothy. Place half of the Ritz cracker and Parmesan mixture in a third bowl for dipping.
Working with one breast at a time, roll in the flour making sure it is thoroughly coated. Dip in the egg and turn until coated. Transfer to the Ritz cracker crumb bowl and turn until the chicken is completely coated. Transfer to a plate or platter. (Can be done several hours in advance at this point. Keep refrigerated until ready to proceed).
Melt the butter with the oil in a large skillet over medium-high heat. Add the Ritz cracker-coated chicken and cook until lightly browned, 3 to 4 minutes per side.
Spread enough of the marinara sauce to thickly coat the bottom of the baking dish. Arrange the chicken on top of the sauce. Spoon the rest of the sauce over each breast and top with the mozzarella cheese and the remaining Ritz cracker and Parmesan mixture. Bake until bubbly and browned, 15 to 20 minutes.