Preheat oven to 375°F (190°C).
In a small bowl, combine broccoli, bell pepper, cheese, and mayonnaise to make the stuffing.
Carefully slice a pocket into each chicken breast without cutting all the way through.
Season the chicken breasts—inside and out—with 1 teaspoon garlic powder, onion powder, paprika, salt, and pepper.
Stuff each chicken breast with the broccoli and cheese mixture, securing with toothpicks if needed.
Heat olive oil in an oven-safe skillet over medium heat. Stir in the remaining 1/2 teaspoon garlic powder.
Sear the stuffed chicken breasts for 3–4 minutes per side until golden brown.
Transfer the skillet to the preheated oven and bake for 20–25 minutes, or until the chicken is cooked through (internal temp of 165°F).
Let rest for a few minutes before slicing and serving.