Preheat oven to 350°F (175°C) and grease a 9×13-inch baking dish.
In a large bowl, combine shredded chicken, steamed broccoli, cream of chicken soup, sour cream, half the cheese, garlic powder, onion powder, salt, and pepper. Mix until smooth and well blended.
In a separate bowl, stir together the stuffing mix, chicken broth, and melted butter until moistened.
Spread the chicken-broccoli mixture evenly in the prepared baking dish.
Spoon the stuffing mixture over the top and spread it out evenly.
Sprinkle the remaining cheddar cheese on top for a golden, gooey finish.
Bake for 30–35 minutes, or until the casserole is bubbly and the top is lightly browned.
Let the casserole rest for 5 minutes before serving for easier slicing.
