Combine season packets from noodles, red pepper, soy sauce, 1/2 cup water and cornstarch, and mix well. Pour over beef strips, stirring to evenly coat meat. Marinate refrigerated for at least 1 hour.
Heat 1 tablespoon oil in wok or non-stick skillet. Stir broccoli pieces in oil for 1 minute. Break noodles into medium size pieces and add to skillet with 1 1/2 cups of water. Cover and simmer for 5 minutes, stirring occasionally. Remove noodles and broccoli from skillet and keep warm.
Heat other tablespoon of oil in skillet. Stir-fry beef with marinade and onions in hot oil for about 2 minutes. Add mushrooms and cook for about 5 more minutes or until beef is no longer pink. Spoon beef and pan juices over noodles and serve.