Preheat oven to 400ºF. Place chicken breasts between two sheets of plastic wrap and firmly pound chicken with a meat mallet to a thickness of ½”; season chicken thoroughly with pepper.
Beat egg in a shallow bowl and set aside. Mix breadcrumbs, ½ cup Parmesan and Italian seasoning in a separate bowl; set aside. Place flour in a sifter or strainer; sprinkle over chicken breasts, evenly coating both sides.
Dip flour coated chicken breast in beaten eggs. Transfer breast to breadcrumb mixture, pressing the crumbs into both sides. Repeat for each breast. Set aside breaded chicken breasts for about 15 minutes.
Heat olive oil in a large skillet on medium-high heat until it begins to shimmer. Cook chicken until golden, about 1 ½ minutes on each side (chicken will finish cooking in oven).
Place chicken on a baking sheet lined with foil and sprayed with Pam®. Spread evenly each breast with tomato paste. Layer each chicken breast with equal amounts of Mozzarella cheese and sprinkle with basil. Top with Parmesan and asiago cheese and add red pepper flakes to taste.
Bake in the preheated oven until cheese is browned and bubbly, and chicken breasts are no longer pink in the center, 12 to 15 minutes. An instant-read thermometer inserted into the center should read at least 165ºF. Serve with pasta or greens.
