Preheat the oven to 375°F.
In a medium bowl, combine the chopped broccoli, shredded cheddar cheese, cream cheese, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Using a sharp knife, create a pocket in each chicken breast by slicing horizontally, being careful not to cut all the way through.
Stuff each chicken breast with the broccoli and cheese mixture, dividing it evenly between the two breasts.
Secure the openings with toothpicks if necessary.
Heat olive oil in an oven-safe skillet over medium-high heat. Once hot, add the stuffed chicken breasts and sear for 3-4 minutes on each side until golden brown.
Transfer the skillet to the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
Remove from the oven and let rest for 5 minutes before serving. Sprinkle with paprika if desired for garnish.