Preheat the oven to 375 degrees F (190 degrees C). Coat an 8-inch square casserole dish with cooking spray.
Combine broccoli, Cheddar cheese, rice, and onion in a medium bowl. Add salt and garlic granules; mix well.
Cut a deep pocket into each chicken breast with a sharp knife. Stuff each breast with broccoli-cheese mixture, place in the prepared casserole, and sprinkle with poultry rub. Cover casserole with aluminum foil.
Place in the preheated oven and bake for 25 minutes. Remove foil and cook until chicken is no longer pink in the center and the juices run clear, about 10 more minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).