Cook noodles according to package directions, omitting salt and fat.
Combine soy sauce and next 3 ingredients in a small bowl; stir well with a whisk.
Place a nonstick skillet coated with cooking spray over medium-high heat until hot; add beef. Stir-fry 4 minutes or until browned. Remove beef from pan; set aside, and keep warm. Coat pan with oil. Add garlic and bell pepper; stir-fry 2 minutes. Add water chestnuts and snow peas; stir-fry 1 minute. Return beef, juices, and soy sauce mixture to pan, and cook 30 seconds or until slightly thickened. Serve over noodles.