Beat eggs in a shallow bowl and set aside. Mix bread crumbs and ½ cup Parmesan cheese in a separate bowl, set aside. Dip a flour-coated chicken breast in beaten eggs. Transfer breast to the bread crumb mixture, pressing crumbs into both sides. Repeat for each breast. Let chicken rest for 10 to 15 minutes.

Heat ½ inch of olive oil in a large skillet over medium-high heat until it begins to shimmer. Cook chicken in batches, until golden, about 2 minutes per side.

Transfer chicken to a baking dish. Top each breast with 2 tablespoons tomato sauce. Layer each chicken breast with equal amounts of mozzarella cheese, fresh basil, and provolone cheese. Sprinkle remaining Parmesan over top and drizzle each with ½ teaspoon olive oil.

Bake in the preheated oven until cheese is browned and bubbly and chicken breasts are no longer pink in the center, about 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Let chicken rest briefly before serving.