Preheat your oven to 350°F (175°C).
In a medium saucepan over medium heat, cook the broccoli until just tender. Drain and set aside.
In a large mixing bowl, combine the cooked rice, shredded chicken, cooked broccoli, cream of chicken soup, sour cream, and milk. Mix well until all ingredients are thoroughly combined.
Add the garlic powder, onion powder, salt, and pepper to the mixture, and stir until evenly distributed.
Transfer the mixture to a greased 9x13 inch baking dish, spreading it out evenly.
Sprinkle the shredded cheddar cheese on top of the casserole.
If desired, sprinkle breadcrumbs over the cheese for added texture.
Cover the baking dish with aluminum foil and place it in the preheated oven.
Bake for 20 minutes, then remove the foil and bake for an additional 10 minutes or until the cheese is bubbly and golden brown.
Allow the casserole to cool for a few minutes before serving.