In a medium bowl or a resealable plastic bag toss together the beef, soy sauce, ground black pepper and cornstarch (this ingredient is used in Chinese cuisine to "velvet" the meat, which tenderizes the meat, keeping it juicy and preventing overcooking). Set the marinated meat aside for 15 -30 minutes. Or allow to marinate for up to 4 hours in the refrigerator.
In a small bowl whisk together the stir fry sauce ingredients. Soy sauce, broth or water, honey or brown sugar, sesame oil, garlic, ginger and cornstarch. Set aside.
In a large wok or large skillet heat 1 tablespoon of oil over high heat (or medium-high heat). Cook the beef in 2 batches, not to overcrowd the wok or skillet.
When the oil is hot, add half of the marinated beef, spreading it on a single layer for even cooking. Sauté for about 2-3 minutes or until lightly golden brown on one side. Toss and continue cooking, stirring frequently for about 1-2 minutes. The steak doesn't have to be fully cooked at this point. Transfer to a bowl and then, sauté the remaining batch (add additional oil if needed). Transfer the steak to the same bowl. Set aside.
Heat the remaining oil. Stir in the onions, red bell pepper and carrots and sauté, stirring often for about 3-4 minutes or until the onions are translucent and the carrots are crisp.
Stir in the broccoli and cook, tossing frequently for about 2 minutes or until crisp tender.
Add the steak back into the wok or skillet with any collected juices. Toss to combine
Pour in the prepared stir fry sauce, and cook for about 2 minutes tossing and stirring frequently. Stir in the scallions and cook, tossing and stirring until the sauce slightly thickens. Remove from the heat and garnish with sesame seeds.Serve immediately with steamed rice (optional)