Toast bread crumbs in large nonstick skillet over medium-high heat until browned, about 5 minutes. Transfer to bowl. Toss with 1 tablespoon olive oil, 1/4 cup Parmesan, and half of basil. In separate bowl, combine remaining olive oil, 1/4 cup Parmesan, remaining basil, garlic, tomatoes, and salt and pepper to taste.
Place flour in dish. Season chicken with salt and pepper and coat with flour. Heat 2 tablespoons vegetable oil in now-empty skillet over medium-high heat until shimmering. Add 4 cutlets and cook until golden brown on both sides, about 5 minutes total. Transfer to plate and repeat with remaining cutlets and vegetable oil.
Reduce heat to medium-low and add tomato mixture to empty skillet. Return cutlets to pan in even layer, pressing down to cover with sauce. Sprinkle mozzarella, provolone, and remaining Parmesan over chicken. Cover with lid and cook until cheese is melted, about 5 minutes. Sprinkle with bread crumb mixture and serve.