Place the sliced round steak in a shallow bowl and toss with the corn starch, 1 teaspoon salt, and ½ teaspoon black pepper. Set aside.
Place the prepared carrots, broccoli and onion in a large bowl. Set aside.
Place the prepared bok choy into a large bowl. Set aside.
In a medium bowl whisk together the soy sauce, hoisin sauce, teriyaki sauce, rice wine vinegar, and the ginger. Set aside.
Heat 1 tablespoon of oil over high heat in the wok. Add in the broccoli, carrots and onion and stir occasionally for approximately 4-5 minutes. Remove the partially cooked vegetables with a large slotted spoon to an awaiting bowl. Keep warm.
Heat another 1 tablespoon oil in the pan and add in the bok choy, garlic and water chestnuts. Cook stirring occasionally for 2-3 minutes. Remove the partially cooked bok choy with a large slotted spoon to an awaiting bowl. Keep warm.
Add the final 1 tablespoon oil to the heated wok and add the prepared beef, stirring occasionally (approximately 3-4 minutes).
Add all the partially cooked vegetables back into the wok along with the soy/teriyaki sauce, and the red pepper flakes (if desired). Season with the remaining salt and pepper, or to taste.
Cook, stirring frequently until everything is heated through (approximately 2-3 minutes).
Serve by spooning the beef and vegetables over prepared brown rice.