Preheat oven to 400°F. Spread chicken and rice in greased 2-quart baking dish.
Mix stock, milk and seasonings in medium bowl with wire whisk until well blended. Slow pour over chicken and rice. Cover with foil.
Bake 45 minutes. Remove foil. Stir in broccoli. Sprinkle with cheese. Bake, uncovered, 15 minutes longer or until rice has absorbed all the liquid and broccoli is tender.