Combine soy sauce, chopped garlic and ginger, sesame oil and black pepper in a large mixing bowl and whisk together. Slice flank steak on a bias, approximately 1/8-inch thick. Add to marinade, cover, and refrigerate for a minimum of 2 hours. When ready to cook, drain marinade from meat.
Lightly oil wok or deep skillet. Grill the beef for 2 minutes. Add the peppers, onions, and broccoli. Continue cooking for 1 to 2 minutes until beef is almost cooked throughout. Add sauce and toss with beef mixture. Coat well and continue to saute for 1 minute. Remove from heat. Garnish beef with green onion straws and serve with steamed jasmine rice.