Preheat oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with butter or cooking spray.
Cook 3 cups rice according to package directions if not using leftovers. Steam 2 cups broccoli florets for 2-3 minutes until just tender and bright green. Drain well and pat dry.
In a large bowl, whisk together 1 can cream of chicken soup, ½ cup sour cream, ½ cup milk, ½ teaspoon garlic powder, ½ teaspoon onion powder, ½ teaspoon paprika, ½ teaspoon salt, and ¼ teaspoon black pepper until smooth and well combined.
Stir in 2 cups cooked chicken, cooked rice, steamed broccoli, and 1 cup shredded cheddar cheese. Mix until everything is evenly coated with the creamy sauce.
Transfer the mixture to the prepared baking dish and spread evenly. Top with the remaining ½ cup cheddar cheese. If using breadcrumbs, mix ½ cup breadcrumbs with 2 tablespoons melted butter and sprinkle over the cheese.
Bake uncovered for 25-30 minutes until hot, bubbly, and the cheese is golden and melted. Let rest for 5 minutes before serving to allow the casserole to set.