Preheat your oven to 350°F. Boil a large pot of water for blanching the broccoli.
In a medium saucepan, add the diced onion and butter. Cook over medium-low heat until softened and translucent, about 5 minutes.
Stir in the flour, garlic powder, and black pepper. Cook for another 2 minutes, then gradually add the milk, whisking to avoid lumps.
Whisk the mixture over medium heat until thick and bubbly. Remove from heat and stir in the dry mustard, paprika, cream cheese, and 1 ½ cups shredded cheddar cheese until melted.
Taste the cheese sauce and adjust seasoning with more salt and pepper if necessary.
Blanch the broccoli in boiling water for 1-2 minutes until bright green and crisp. Drain well.
In a large bowl, combine the cooked rice, blanched broccoli, and cheese sauce, ensuring everything is well-coated.
Transfer the mixture to a greased 2-quart casserole dish and top with remaining cheddar cheese.
Bake in the preheated oven for 35 minutes or until the cheese is bubbly and lightly browned.