In a small bowl, combine the garlic salt, onion powder, and paprika. Rub the seasoning mixture all over the chicken breasts.
Place the chicken breasts on a parchment paper lined tray. Carefully cut a pocket into the side of each chicken breast, making sure not to slice all the way through.
In a medium bowl, combine the cream cheese, Parmesan cheese, cheddar cheese, minced garlic, and chopped broccoli. Mix until fully combined. Using your hands works best for evenly mixing the filling.
Scoop about 6–7 tablespoons of the broccoli cheese mixture into each chicken breast pocket. Repeat with all four chicken breasts.
Heat the butter and vegetable oil in a large skillet over medium-high heat.
Once hot, add the stuffed chicken breasts to the skillet. Sear for 4–5 minutes per side until golden brown.
Reduce the heat to low and cover the skillet with a lid. Cook for about 15 more minutes, or until the chicken is fully cooked and reaches an internal temperature of 165°F.
Serve warm over mashed potatoes if desired.