Combine ginger, garlic, soy sauce, 2 teaspoons cornstarch, oil, and crushed red pepper in a large zip-top bag; add steak to bag. Seal and marinate in refrigerator 20 minutes.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray, and add mushrooms, onion, and bell pepper to pan. Cook 3 minutes or until crisp-tender; transfer to a large bowl. Add bok choy to pan; sauté 2 minutes or until slightly wilted; add to bowl; keep warm.
Recoat pan with cooking spray. Add half of steak mixture to pan; cook 3 minutes or until browned, stirring occasionally. Transfer to a large bowl; keep warm. Coat pan with cooking spray. Add remaining steak mixture to pan; cook 3 minutes or until browned, stirring occasionally. Add to bowl; keep warm.
Combine broth and remaining 2 teaspoons cornstarch, stirring with a whisk. Add to pan, scraping pan to loosen browned bits. Bring to a boil; cook 1 minute or until mixture thickens, stirring constantly. Return steak and vegetables to pan; toss gently to coat.