Preheat oven to 350°F and grease a 9x13-inch casserole dish.
Bring a medium pot of water to a boil. Add the broccoli and cook for 3 to 5 minutes until tender. Drain the broccoli.
In a large skillet over medium heat, melt the butter and cook the onion until softened, about 4 to 6 minutes. Stir in the cream of mushroom soup, cream of cheddar cheese soup, milk, 1 cup cheddar cheese, and Parmesan cheese. Cook until all the cheese has melted. Mix the broccoli and cooked rice, and transfer to the prepared casserole dish. Top the mixture with the remaining cheddar cheese, then cover with aluminum foil.
Bake for 25 to 30 minutes until the cheese is bubbly and melted.
Notes
Freshly shredded cheese melts smoother than pre-shredded cheese
Frozen broccoli can be used if needed
Add cooked chicken or ham to turn this into a full meal
Crushed Ritz crackers or potato chips make a great crunchy topping
Covering with foil helps keep the casserole creamy while baking
Let the casserole sit a few minutes before serving so it sets up slightly