Combine rice and broccoli in large mixing bowl. Cook mushrooms, onion and garlic in oil over medium heat until onion is tender crisp. Add salt, pepper and nutmeg. Stir mixture into rice and broccoli; mix well. Spoon into shallow 2-quart baking pan. Beat egg yolks with milk. Add cheese. 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 degrees 30 minutes or until mixture is hot and bubbly and top is lightly browned (15 to 20 minutes for casseroles).