Preheat the oven to 350°F (175°C).
Lightly grease a 9×13 inch casserole dish with butter or cooking spray.
Steam the broccoli florets until tender but still crisp, about 4-5 minutes. Drain and set aside.
In a large mixing bowl, combine the cooked rice, shredded chicken, steamed broccoli, cream of mushroom soup, sour cream, milk, garlic powder, onion powder, salt, and black pepper. Mix well until fully combined.
Add the shredded cheddar cheese and half of the mozzarella cheese to the mixture and stir to incorporate evenly.
Transfer the mixture into the prepared casserole dish and spread it out evenly.
Sprinkle the remaining mozzarella cheese and the grated Parmesan cheese evenly over the top of the casserole.
Drizzle the melted butter over the cheese layer to help it brown nicely.
Bake uncovered in the preheated oven for 30-35 minutes, or until the casserole is bubbly and the cheese is melted and golden brown on top.
Remove from the oven and let it rest for 5 minutes before serving.