Preheat the oven to 350°F (175°C).
In a medium saucepan, melt the butter over medium heat.
Add the Chicken Rice-A-Roni pasta and seasoning mix from the box to the melted butter. Cook and stir for 2-3 minutes until the pasta is lightly browned.
Add 1 cup water to the saucepan, bring to a boil, then reduce heat to low and cover. Simmer for 15 minutes or until the rice is tender and liquid is absorbed.
While the rice cooks, steam the broccoli florets until tender-crisp, about 4-5 minutes. Drain and set aside.
In a large mixing bowl, combine the cooked rice mixture, cooked chicken, steamed broccoli, condensed cream of mushroom soup, sour cream, chopped onion, garlic powder, black pepper, salt, and half of the cheddar and mozzarella cheeses. Mix well until all ingredients are evenly combined.
Transfer the mixture into a greased 9×13-inch casserole dish and spread evenly.
Sprinkle the remaining cheddar and mozzarella cheeses and the grated Parmesan cheese evenly over the top.
Bake uncovered in the preheated oven for 20-25 minutes, or until the casserole is bubbly and the cheese on top is melted and golden brown.
Remove from the oven and let it rest for 5 minutes before serving.