Preheat your oven to 375°F (190°C).
In a small bowl, mix the chopped broccoli, shredded cheddar, cream cheese, garlic powder, and onion powder until well combined.
Using a sharp knife, carefully cut a pocket into the side of each chicken breast. Season the chicken all over with salt, pepper, and paprika.
Stuff each chicken breast with the broccoli cheese mixture. Secure the openings with toothpicks if needed to keep the filling inside.
Heat olive oil in a large oven-safe skillet over medium-high heat. Sear the stuffed chicken breasts for 2–3 minutes per side until golden brown.
Transfer the skillet to the preheated oven and bake for 15–20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Remove the toothpicks, let the chicken rest for a few minutes, then slice and serve.