Preheat your oven to 375°F and grease a 9x9 baking dish.
In a skillet over medium heat, melt the butter.
Add the diced onion and cook until soft and translucent.
Stir in the cream of chicken soup, Cheez Whiz, and milk.
Add the garlic powder and black pepper, stirring until everything is smooth and heated through.
Cook the frozen broccoli according to the package directions, then add it to the cheese mixture.
Use a spoon to break up any large pieces of broccoli so it is evenly distributed.
Stir in the cooked white rice until everything is well combined.
Transfer the mixture to the prepared baking dish and spread it evenly.
Sprinkle the shredded cheddar cheese over the top.
Bake for about 30 minutes, until the casserole is hot and bubbly and the cheese is melted.
Remove from the oven and let it rest for a few minutes before serving.