Cook onion and butter on medium-low heat until softened and translucent. Stir in flour, garlic powder, and black pepper. Cook an additional 2 minutes.
Gradually pour in milk while whisking. Continue whisking over medium heat until thick and bubbly. Remove from heat and add dry mustard, paprika, cream cheese, and 1 1/2 cups cheddar cheese. Stir until melted. Taste and season the sauce with salt.
Place broccoli in boiling water for about 2 minutes. You still want it slightly crisp as it cooks more in the oven.
Stir together rice, broccoli, and cheese sauce. Place in a greased 2-quart casserole dish. Top with remaining cheese and bake for 35 minutes or until bubbly and cheese is lightly browned.