Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish.
In a separate bowl, mix the stuffing mix with the chicken broth and melted butter. Allow it to sit for 5-7 minutes until the stuffing is fully soaked and fluffy.
In a large bowl, combine shredded chicken, cream of chicken soup, sour cream, garlic powder, pepper, and thyme. Mix well until creamy and evenly incorporated.
If you're adding broccoli, fold it into the chicken mixture until combined.
Spread the chicken mixture evenly in the prepared baking dish. Top it with the prepared stuffing mix, spreading it out evenly.
Bake uncovered for 35-40 minutes, or until the top is golden brown and the casserole is bubbling around the edges.
Let the casserole cool for about 5-10 minutes before serving so it holds together better.