Thaw broccoli and warm broccoli in the microwave for about 5 minutes; drain very well. Cut any large florets into smaller, bite-sized pieces.
In a bowl, combine warm cooked rice, onion, cream of mushroom soup, milk, salt, pepper, garlic powder, paprika, and 1 cup of the shredded cheddar. Stir together until well mixed. Fold in broccoli.
Spoon into a greased 9x13-inch baking dish. Top with remaining 1 cup shredded cheddar cheese.
Bake at 350℉ for 35 - 40 minutes until bubbly and cheese is just beginning to get some golden brown spots.
Casserole may be prepared ahead. Place the broccoli mixture in the casserole dish, top with the cheese, and refrigerate until ready to bake. Increase baking time to 60 - 75 minutes. Cover loosely with foil partway through baking if the cheese begins to brown too much.
