Combine rice and broccoli in large mixing bowl.
Cook mushrooms, onion and garlic in butter over medium heat until onion is tender crisp. Add 1/2 tsp salt, 1/4 tsp pepper and 1/8 tsp nutmeg. Stir mixture into rice and broccoli; mix well. Spoon into buttered shallow 2-quart baking pan or portion 1 cup mixture into buttered individual casseroles.
Beat egg yolks with milk. Add cheese, remaining 1/2 tsp salt, remaining 1/4 tsp pepper and remaining 1/8 tsp nutmeg.
Beat egg whites until stiff but not dry. Fold into yolk mixture. Spread over rice mixture, or portion evenly over rice mixture in individual dishes (about 2/3 cup for each).
Bake at 350° F 30 minutes, or until mixture is hot and bubbly and top is lightly browned - 15 to 20 minutes for casseroles).
Servings: 6