In bowl, combine soy sauce, 2 teaspoons cornstarch, and beef. Refrigerate 30 minutes. Place broccoli in large bowl, cover, and microwave 3 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. Add remaining beef; brown and transfer to bowl.
Dissolve remaining cornstarch in 1 tablespoon water. Heat remaining oil in skillet; add ginger, garlic, and carrots. Cook 1 minute, then stir in broth and oyster sauce; bring to a boil. Whisk in cornstarch; cook 1 minute. Stir in beef and broccoli.