Preheat oven to 400°F (200°C) and lightly grease a 9x13 inch baking dish.
In a large bowl, toss the sliced bell peppers and red onion with 1 tablespoon of olive oil and a pinch of salt.
Place chicken breasts in the prepared baking dish. Rub both sides with the remaining olive oil, minced garlic, oregano, smoked paprika, salt, and black pepper.
Arrange the seasoned pepper and onion mixture around and over the chicken breasts.
Bake in the preheated oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Sprinkle the shredded mozzarella cheese evenly over the chicken and vegetables.
Return to the oven for 5 minutes or until the cheese is melted and bubbling.
Garnish with fresh basil before serving.