Preheat the oven to 375°F (190°C). Lightly oil a baking dish.
Butterfly each chicken breast: place hand flat on top, slice horizontally about 3/4 of the way through to create a pocket. Don’t cut all the way.
In a bowl, combine roasted red peppers, chopped spinach, minced garlic, mozzarella, oregano, salt, and pepper. Mix gently.
Stuff each chicken pocket with about 1/4 of the filling. Secure with toothpicks or tie with kitchen twine. Brush outside with olive oil and sprinkle a little extra salt and pepper.
Place stuffed breasts in the prepared dish. If you like, sprinkle Parmesan over the tops.
Bake for 25–30 minutes, or until the internal temperature reaches 165°F (74°C) and juices run clear. If the cheese isn’t browned to your liking, broil for 1–2 minutes—watch closely.
Let chicken rest 5 minutes before slicing. Remove toothpicks or twine and serve.
Notes
Don’t overstuff the chicken. Use a meat thermometer for best results.