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