Cut beef steak lengthwise in half, then crosswise 1/8 to 1/4 inch thick . Toss beef with 1 tablespoon cornstarch in large bowl. Add marinade ingredients to bowl; toss to evenly coat beef. Cover and marinate in refrigerator 30 minutes.
Heat 1 teaspoon vegetable oil in large nonstick skillet on medium-high until hot. Add onion and garlic; stir fry 2 to 3 minutes or until onion begins to brown. Remove from skillet to large bowl. Remove beef from marinade; discard marinade. Heat 1 teaspoon vegetable oil in same skillet until hot. Add a third of the beef with third of ginger; stir-fry 2 to 3 minutes until outside surface of beef is no longer pink. Add to bowl with onion. Repeat twice with remaining oil, beef and ginger.
Dissolve remaining 1 tablespoon cornstarch in cold water in small bowl. Set aside. Heat broth, pepper, soy sauce, oyster sauce and corn starch mixture to same skillet. Bring to a boil, stirring constantly, until sauce is thickened and bubbly. Reduce heat; simmer 5 minutes to desired thickness.
Add beef mixture and broccoli to skillet. Cook and stir until heated through. Serve over rice or noodles. Garnish with toasted sesame seeds or drizzle with sesame oil, if desired.
Nutrition information per serving: 357 Calories; 81 kcal Calories from fat; 9 g Total Fat; 3 g Saturated Fat; 3 g Monounsaturated Fat; 66 mg Cholesterol; 555 mg Sodium; 39 g Total Carbohydrate; 3.1 g Dietary Fiber; 30 g Protein; 2.7 mg Iron; 7.6 mg Niacin; 0.7 mg Vitamin B6; 1.4 mcg Vitamin B12; 4.8 mg Zinc; 30.3 mcg Selenium; 95.4 mg Choline;