Preheat the oven to 350 degrees and lightly grease a 9 by 13 inch baking dish.
In a large mixing bowl, combine the cooked rice, shredded chicken, steamed broccoli florets, sour cream, milk, garlic powder, salt, and black pepper.
Stir in 1 cup of the shredded cheddar cheese until everything is evenly coated.
Transfer the mixture to the prepared baking dish and spread it into an even layer.
Sprinkle the remaining 1/2 cup of cheddar cheese over the top.
Bake for 25 to 30 minutes until the cheese is melted and the edges are lightly golden.