Heat outdoor grill or indoor grill pan to high. Season chicken with salt and pepper and drizzle with extra-virgin olive oil to keep it from sticking to the grill. Cook 3 to 4 minutes on each side and transfer to a foil covered platter to hold. If you are using a grill pan, cook the chicken in 2 batches if necessary. While chicken cooks, make sauce.
Place a medium pot on the stove over medium heat. Add 2 tablespoons extra-virgin olive oil, 2 turns of the pan. Add garlic, crushed red pepper flakes and chopped onions. Cook 10 minutes, stirring often. Add tomatoes and heat through, 2 minutes. Wilt in the basil and season the sauce with salt and pepper.
Preheat the broiler to high.
Layer the chicken with fire roasted sauce in a casserole dish. Top the casserole with Parmigiano and mozzarella. Brown the casserole under the broiler 3 minutes.