Preheat the oven to 350°F (175°C).
Steam the broccoli florets until tender but still crisp, about 4-5 minutes. Drain and set aside.
In a large mixing bowl, combine the shredded cooked chicken, steamed broccoli, cream of mushroom soup, sour cream, mayonnaise, chopped onion, garlic powder, black pepper, salt, cooked white rice, and shredded cheddar cheese. Mix well until all ingredients are evenly incorporated.
Transfer the mixture into a greased 9×13-inch casserole dish and spread evenly.
Sprinkle the shredded mozzarella cheese evenly over the top of the casserole.
In a small bowl, mix the crushed Ritz crackers with the melted butter until the crumbs are evenly coated.
Sprinkle the buttered cracker crumbs evenly over the mozzarella cheese layer.
Cover the casserole dish tightly with aluminum foil if freezing, or bake uncovered if cooking immediately.
To freeze: Place the covered casserole in the freezer for up to 3 months. When ready to bake, thaw overnight in the refrigerator.
To bake: Bake uncovered at 350°F (175°C) for 40-45 minutes or until the casserole is bubbly and the topping is golden brown.
Remove from the oven and let it rest for 5 minutes before serving.