In a large skillet, melt the butter. Add the onion and garlic and cook, stirring with a wooden spoon, until softened, 3 to 4 minutes. Sprinkle over the flour, dry mustard and cayenne and stir to mix it in well. Continue to cook for 1 minute.
Next, add the milk, stirring constantly; cook until thickened, about 2 minutes. Add the cream cheese and Parmesan, stirring until totally combined. Stir in the pepper, salt and paprika. Add the processed cheese, stirring until completely melted. Next, add 1 1/2 cups of the Cheddar and stir until melted. Then, fold in the broccoli and pimentos.
In a large baking dish, create a base with half of the rice. Top with half of the broccoli cheese sauce. Repeat with the remaining rice, then the remaining sauce. Sprinkle the rest of the Cheddar evenly over the top of the casserole. Bake until bubbly, about 30 minutes.