Preheat oven to 400°F. Grease a 13x9-inch, broiler-safe casserole.
Butterfly chicken breast halves: Slice through each breast horizontally, leaving 1⁄4-inch “hinge.”
Open chicken breasts and place in casserole. Sprinkle with half of Italian seasoning and salt and pepper. On one side (half) of each breast, layer roasted red peppers, basil leaves, and 1 slice mozzarella. Fold over other side, tucking in fillings. Sprinkle with remaining Italian seasoning.
Bake for 30 to 40 minutes, or until internal temperature of chicken breast reaches 165°F on an instant-read thermometer. Remove from oven. Turn oven to broil. Top each breast with 1 slice mozzarella. Sprinkle with Parmesan. Broil until cheese is browned and bubbly, about 5 minutes.