Grease a 9x13-inch casserole pan. Preheat oven to 400°F.

In a large saucepan melt the butter over low heat; add garlic and saute until fragrant. Whisk in flour and cook 3-4 minutes, whisking constantly. Slowly whisk in milk, mustard and season with salt and pepper, bring to a simmer 4 minutes, whisking occasionally. Add 2 cups of cheddar cheese and parmesan; stir until mostly melted; remove from heat.

Stir in rice and broccoli florets, pour into casserole pan, sprinkle remaining 1/2 cup cheese over top. Bake 30 minutes until bubbly and lightly golden on top. Allow to set 5 minutes before serving.