Preheat the oven to 375°F and lightly grease a 9x13-inch baking dish.
Steam the broccoli until just tender, then set it aside.
In a large bowl, mix the chicken, rice, broccoli, cream of chicken soup, milk, garlic powder, onion powder, salt, and pepper.
Stir in half of the shredded cheese, then spread the mixture evenly in the baking dish.
Sprinkle the remaining cheese over the top.
Mix the breadcrumbs with the melted butter and sprinkle evenly over the casserole.
Bake for 30 to 35 minutes, until bubbly and lightly golden on top.