In bowl, combine 2 tablespoons teriyaki sauce, 2 teaspoons cornstarch, and beef. Refrigerate 30 minutes, or up to 10 hours. Place broccoli and carrots in large bowl and cover tightly. Microwave 5 minutes.
In nonstick skillet, heat 1 teaspoon oil over high heat. Add half of beef and cook, stirring until browned, about 2 minutes. Transfer to bowl with broccoli. Repeat with remaining beef.
Dissolve remaining cornstarch in 1 tablespoon water. Heat remaining oil in skillet; add ginger and garlic. Cook 30 seconds, then stir in broth and remaining teriyaki sauce; bring to a boil. Whisk in cornstarch mixture; boil 1 minute. Stir in beef, broccoli, and carrots; heat through. Spoon over barley.