Warm the cooked rice and set it aside.
Blanch fresh broccoli until tender and bright, or thaw and drain frozen broccoli.
In a pan, sauté onion and garlic until soft.
Add butter, then stir in flour to form a roux.
Slowly whisk in chicken broth and cream until thick and smooth.
Lower heat and stir in cheeses until melted. Season well.
Fold rice and broccoli into the cheese sauce.
Transfer mixture to a greased baking dish.
Cover and bake at 350°F for 25 minutes.
Uncover and bake 15 minutes more until bubbly and golden.
Rest 10 minutes before serving.