In a 3-1/2- or 4-quart slow cooker, combine beef, beef broth, water, sweet peppers, water chestnuts, green onions, soy sauce, ginger, and black pepper.
Cover and cook on low-heat setting for 6 to 8 hours or on high-heat setting for 3 to 4 hours. Turn off cooker. Stir in noodles. Cover and let stand for 5 minutes. If desired, top with green onion strips.