Season both sides of the chicken breasts with salt, pepper, paprika and 1/2 tsp of the garlic powder. Use a sharp knife to cut a slice through the middle of the chicken breasts, but not all the way through, creating a pocket for the filling.
For the filling, place the broccoli in a microwaveable dish and add about 2 tablespoons of water. Cover with plastic wrap and microwave for 1 minute. Drain any excess water. To the dish add the bell pepper, cheese, mayo, remaining garlic powder and salt and pepper to taste. Mix until combined, then divide the mixture between the chicken breasts, using a toothpick to secure if necessary.
Heat a large, oven safe skillet (I prefer to use a cast iron skillet), over medium heat and add the olive oil. Sear the chicken for 3 to 4 minutes on each side. Cover skillet with foil and bake in preheated oven for 15- 17 minutes, or until chicken reads 165 degrees. Let rest, covered for 5 minutes before enjoying.
*Since these are large chicken breasts, I usually say 1/2 chicken breast is one serving.