Add steak to re-sealable plastic bag along with soy sauce, ginger, garlic and pepper. Marinate, refrigerated, 2 hr. or overnight.
Remove steak from marinade, pouring marinade from the bag into a bowl. Pat steak dry with paper towel. Heat half the oil in large skillet set over medium-high heat. Cook steak 8 to 10 min., turning once, or until medium-rare and internal temperature reaches 145°F (63°C). Transfer steak to plate to rest.
Meanwhile, whisk together reserved marinade and flour until smooth. Stir in beef broth and 1/4 cup (60 mL) water; set aside.
Heat remaining oil in same skillet set over medium-high heat. Add green beans and cook, stirring, 2 to 3 min. until they start to soften. Reduce heat, if necessary, to prevent scorching browned bits in bottom of skillet. Stir in bok choy; cook 2 to 3 min. until tender-crisp. Transfer vegetables to plate. Pour marinade mixture into skillet; bring to a boil. Reduce heat to medium-low. Simmer 3 to 5 min. until thickened. Add green beans and bok choy back into skillet; cook another 1 to 2 min. until tender. Transfer beans and bok choy to serving dish. Thinly slice steak across the grain; place on vegetables. Drizzle with sauce remaining in skillet to serve.
Garnish with thinly sliced green onion, fresh chilies or toasted sesame seeds.
Substitute flour with cornstarch for gluten-free sauce option.
Reheat any leftovers and serve over rice or rice noodles.