Preheat an oven to 230 degrees Celsius. Place chicken breasts between two plastic sheets (resealable freezer bags work well) on a solid, level surface. Firmly flatten chicken with flat side of meat mallet. Season the chicken thoroughly with salt and pepper.
Beat the eggs in a shallow bowl and set aside. Mix breadcrumbs and 1/2 cup Parmesan cheese in separate bowl, set aside. Then place the flour in a sieve or strainer; sprinkle over chicken breasts, evenly coating both sides.
Dip flour-coated chicken breast in beaten eggs. Then roll them into the breadcrumb mixture, pressing the crumbs on both sides. Repeat for each portion.
Heat 1 cup olive oil in a large skillet over medium-high heat until just shimmering. Cook chicken until golden brown, about 2 minutes on each side. The chicken will finish cooking in the oven.
Place chicken in a baking dish and cover each breast with about 1/3 cup of tomato sauce. Layer each chicken breast with equal amounts of mozzarella cheese, fresh basil, and provolone cheese. Sprinkle 1 to 2 tablespoons of Parmesan cheese on top and drizzle with 1 tablespoon of olive oil.
Bake in preheated oven until cheese is golden brown and bubbly and chicken breasts are no longer pink in the center, 15 to 20 minutes. An instant read thermometer inserted into the center should read at least 74 degrees Celsius.
Notes
Breast fillets au gratin with an exquisite juicy layer of Parmesan cheese.