Combine 2 tablespoons teriyaki sauce, 2 teaspoon cornstarch, and the beef in a small bowl. Refrigerate 15 minutes, or up to 10 hours. Place broccoli and peppers in large bowl and cover tightly. Microwave on medium-high 5 minutes.
In large nonstick skillet, heat 1 teaspoon oil over high heat. Add beef and cook, stirring, until browned, about 2 minutes. Transfer to bowl with cooked vegetables.
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 and boil 1 minute. Stir in beef, broccoli, and peppers, and cook until just heated through. Serve over brown rice.