Beef and Broccoli Stir Fry

3 T teriyaki sauce, divided
3 T cornstarch, divided
1 pound lean beef, such as top sirloin, sliced for stir fry
4 cups broccoli florets
1 cup sliced carrots
2 t oil, divided
1 t grated fresh ginger
2 garlic cloves, minced
1 cup chicken broth

Combine 2 T teriyaki sauce, 2 t cornstarch, and beef.  Refrigerate 30 minutes, or up to 10 hours.  Place broccoli and carrots in large bowl and cover tightly.  Microwave 5 minutes.
Heat 1 t oil in a large skillet 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 into 1 T 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.
Serve over rice.