Preheat the oven to 350°F (175°C).
Steam the broccoli florets until tender but still crisp, about 5 minutes. Drain and set aside.
In a large bowl, combine the cream of mushroom soup, sour cream, milk, garlic powder, onion powder, salt, and black pepper. Mix until smooth.
Lightly grease a 9×13 inch baking dish with butter.
Spread half of the cooked rice evenly on the bottom of the prepared baking dish.
Layer half of the shredded chicken evenly over the rice.
Spread half of the steamed broccoli evenly over the chicken layer.
Pour half of the creamy soup mixture evenly over the broccoli.
Sprinkle half of the shredded cheddar and mozzarella cheeses evenly over the top.
Repeat the layering process with the remaining rice, chicken, broccoli, soup mixture, and cheeses.
Sprinkle the grated Parmesan cheese evenly over the top layer of cheese.
Dot the top with small pieces of the remaining butter.
Cover the casserole with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 10 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let the casserole rest for 5 minutes before serving.