Preheat the oven to 400°F (200°C).
Pat the chicken breasts dry with a paper towel. Cut a horizontal slit in the thickest part of each breast to create a pocket, ensuring you don’t cut all the way through.
Rub the chicken breasts with the oregano, paprika, salt, and pepper, making sure both sides are coated evenly.
In a small bowl, mix together the chopped broccoli, cheddar cheese, sour cream, garlic powder, and mustard powder.
Stuff each chicken breast with the broccoli and cheese mixture. Use toothpicks to close the pockets.
Heat olive oil in a large oven-safe skillet over medium-high heat. Add the stuffed chicken breasts and sear for about 3 minutes on each side, or until golden brown.
Transfer the skillet to the preheated oven, uncovered, and bake for 15-18 minutes, or until the chicken is fully cooked.
Use an instant-read thermometer to ensure the chicken reaches an internal temperature of 165°F.