Cut steak diagonally across grain into 1/8 inch thick strips and place in a bowl.
Combine soy sauce and next 4 ingredients. Reserve half of mixture. Pour remaining mixture over steak. Cove and marinate in refrigerator 30 minutes.
Drain steak, discarding marinade.
Stir-fry half of steak in 1/2 T hot oil in a large nonstick skillet or wok over medium-high heat 1 minute or until outside of beef is no longer pink. Remove from skillet; repeat procedure with remaining steak and oil. Remove from skillet, and set aside.
Add green onions and water chestnuts to skillet stir-fry 3 minutes or until crisp-tender.
Whisk cornstarch into reserved soy sauce mixture; stir into vegetables, and stir-fry until thickened.
Add steak; stir-fry until thoroughly heated. Serve over noodles or rice.