01 - Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish with 1 tablespoon of the olive oil, coating the bottom and sides evenly.
02 - Arrange the sliced red, yellow, and green bell peppers along with the red onion in an even layer across the bottom of the prepared baking dish. Drizzle with the remaining 1 tablespoon of olive oil, then sprinkle with half of the salt, black pepper, Italian seasoning, and smoked paprika. Toss the vegetables gently to coat them evenly in the oil and seasonings.
03 - Pat the chicken breasts dry with paper towels. Season both sides of each breast with the remaining half of the salt, black pepper, Italian seasoning, and smoked paprika, pressing the spices gently into the meat.
04 - Place the seasoned chicken breasts on top of the bed of vegetables in the baking dish. Scatter the minced garlic evenly over the chicken and the surrounding vegetables.
05 - Cover the baking dish tightly with aluminum foil and place in the center of the oven. Bake for 20 minutes, allowing the chicken to cook through partially while the vegetables soften and release their juices.
06 - Carefully remove the foil from the baking dish. Sprinkle the shredded mozzarella and grated Parmesan cheeses evenly over the top of each chicken breast. Return the dish to the oven, uncovered, and bake for an additional 10 minutes, or until the chicken reaches an internal temperature of 165°F and the cheese is fully melted with golden-brown spots on top.
07 - Remove the baking dish from the oven and let the chicken rest for 5 minutes before serving. This allows the juices to redistribute throughout the meat. Serve each chicken breast over a portion of the roasted peppers and onions, spooning any pan juices over the top.