To steam broccoli: Chop the broccoli florets into small pieces. Put all the broccoli in a microwave-safe bowl and about 2 tablespoons water. add water. Cover with plastic wrap and microwave on high for 2-3 minutes. Alternatively, steam on stove-top or blanch in boiling water for 1 minute.
Use a sharp knife to slice each chicken breasts horizontally to form a pocket. Be sure not stop cutting about 1/2 inch from the ends and sides. Season chicken breasts with a generous sprinkle of Italian seasoning, garlic powder, paprika, salt, and pepper.
In a large bowl, combine the steam and chopped broccoli, bell pepper, garlic, cheeses and salt & Pepper; set aside. Spoon the mixture into each chicken breast evenly. Secure with toothpicks if needed.
Preheat oven to 400F. Heat 1 tablespoons oil in a large cast iron or oven-safe pan over medium-high heat. Add the chicken breasts and cook for 2-3 minutes per side or until golden. Cover with aluminum foil and transfer to preheated oven for 15-20 minutes or until cooked through.