Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large bowl, combine cooked rice, chicken, broccoli, cream of chicken soup, sour cream, milk, and 1 cup of shredded cheese.
Add garlic powder, onion powder, salt, and pepper to taste. Stir until evenly mixed.
Pour the mixture into the prepared baking dish and spread evenly.
Top with remaining cheese, and cover loosely with foil (optional for a softer top).
Bake for 25–30 minutes, or until bubbly and heated through.
Remove foil during the last 5 minutes to lightly brown the top if desired.
Let sit for 5 minutes before serving.