First, preheat your oven to 425 degrees F. Season both sides of the chicken breasts generously with salt, pepper, paprika, and about half a teaspoon of the garlic powder. Using a sharp knife, carefully slice a pocket into the thickest part of each chicken breast, being careful not to cut all the way through.
To prepare the filling, place your finely chopped broccoli in a microwave-safe dish with about two tablespoons of water. Cover it and microwave for just one minute to slightly soften it, then drain any excess water. To the bowl, add the diced red bell pepper, shredded cheddar cheese, mayonnaise, the remaining garlic powder, and a pinch of salt and pepper.
Mix the filling ingredients until they are well combined. Carefully divide the cheesy broccoli mixture among the three chicken breasts, stuffing it into the pockets you created. If you overstuffed them slightly, you can use a toothpick to help seal the pocket and keep the filling from spilling out during cooking.
Heat the olive oil in a large, oven-safe skillet over medium-high heat. Once the oil is shimmering, carefully place the stuffed chicken breasts in the pan and sear them for 3 to 4 minutes on each side until they are golden brown. Cover the skillet with foil and transfer it to the preheated oven. Bake for 15-17 minutes, or until the chicken is cooked through and reaches an internal temperature of 165 degrees F.
Once cooked, remove the chicken from the oven and let it rest, still covered, for at least 5 minutes. This crucial step allows the juices to redistribute, ensuring every bite is moist and tender. After resting, remove any toothpicks, slice the chicken, and serve it warm.