Preheat oven to 350 degrees F.
Grease a 9x13 inch baking dish and set aside.
Place a large skillet over medium heat, add butter and melt it. Once melted, add diced onion and cook, stirring for 1 minute. Add garlic and cook for another 30 seconds.
Stir in flour and cook an additional 2-3 minutes.
Gradually add the milk, stirring it all the time. Next, gradually stir in the cream.
Add the dry mustard, paprika, salt, and pepper. Whisk, reduce heat to low and simmer the mixture until thick and bubbly.
Remove from heat and stir in cream cheese, sour cream and 1 cup of cheddar cheese, until fully melted.
In a large bowl stir together the broccoli, rice, and the sauce ingredients.
Transfer to the prepared casserole dish.
Top with remaining cheddar cheese.
Bake for 30-35 minutes or until bubbly and cheese is slightly browned.