Arrange an oven rack in the middle position and preheat the broiler (or grill) to medium.
Pat chicken dry and season all over with the Italian seasoning, paprika, onion powder, salt, and pepper.
Heat the olive oil in a large skillet over medium heat. Add the chicken and cook until browned and cooked through, about 8 minutes per side depending on thickness. Transfer cooked chicken to a plate and set aside.
In the same skillet, add the chopped onion and cook, scraping up any browned bits, until translucent, about 3–4 minutes. Add the minced garlic and cook until fragrant, about 1 minute.
Add the chopped fire-roasted pepper, crushed tomatoes (or passata), tomato paste, crushed red pepper flakes (if using), and the remaining Italian seasoning. Stir to combine.
Bring the sauce to a simmer and cook, stirring occasionally, until slightly thickened, about 4 minutes.
Return the chicken to the skillet, spoon sauce over each breast, and top each with about 2–3 tablespoons of shredded mozzarella.
Place the skillet (or transfer to an oven-safe dish) under the broiler for 1–2 minutes, until the cheese is browned and bubbly. Watch closely to avoid burning.
Garnish with chopped parsley and serve immediately.