Bring a large pot of water to boil. Add broccoli and boil for 2-3 minutes. Drain and set aside.
Melt butter in a medium saucepan over medium heat. Whisk in flour, garlic powder, dry mustard and paprika and cook for several minutes until golden. Add milk and bring to a simmer until thickened. Remove from heat and stir in cream cheese, 1 ½ cups of cheddar cheese and ½ cup Parmesan cheese. Stir in salt and black pepper; taste and adjust seasoning as desired.
Stir rice, broccoli and cheese sauce together. Pour into a greased 2 quart baking dish and top with remaining cheddar cheese.
Bake uncovered at 350 degrees for about 25-35 minutes, or until the sauce is bubbly and the top is golden. Let cool for 5-10 minutes before serving.