In a large saucepan, combine the broth, apple and raisins. Bring to a boil. Reduce heat; simmer, uncovered for 3-4 minutes or till apple is tender. Stir in butter and stuffing mix. Remove from the heat; cover and let stand for 5 mins.
Sprinkle chicken with salt and pepper. In a large skillet, cook the chicken, mushroom and onion in oil over medium heat till chicken is no longer pink. Add garlic; cook 1 minute longer. Remove from the heat. Stir in sour cream and soup.
Transfer to a 13x9 baking dish coated with cooking spray. Layer with broccoli and stuffing mixture. Bake uncovered at 350* for 20-25 minutes or till heated through.