Preheat the oven to 350 degrees F (180 degrees C). Lightly grease a casserole dish and arrange chicken in a single layer.
Stir soup, sour cream, and onion soup mix together in a bowl and spread evenly over chicken. Sprinkle with pepper.
Combine stuffing mix and chicken broth in a bowl. Spread stuffing mixture over chicken and top with pats of butter.
Bake in the preheated oven until golden and bubbly, and chicken is no longer pink at the center, 50 to 60 minutes. An instant-read thermometer inserted into the center of chicken should read at least 165 degrees F (74 degrees C).
Let stand 10 minutes; sprinkle with parsley. To serve, place chicken and stuffing on individual plates and spoon over about ¼ cup of gravy from the casserole dish.
