Cut steak across the grain into 1/8-inch-thick strips, and place in a medium bowl.
Combine soy sauce and next 4 ingredients. Reserve half of mixture. Pour remaining half of mixture over steak. Cover and chill 30 minutes.
Drain steak, discarding marinade.
Stir-fry half of steak in 1/2 tablespoon 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, and repeat procedure with remaining oil and steak. Remove from skillet.
Add green onions and carrot to skillet, and 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, and stir-fry until thoroughly heated. Serve over noodles or rice. Garnish, if desired.