Mix all the sauce ingredients together. Set aside.
In a large skillet or wok, heat 1 tablespoon oil over high heat until sizzling hot. Add the sesame oil, let it heat for a few seconds then add the beef in an even layer in the pan. Let sit undisturbed for 30 seconds then start flipping and stirring for another 3 minutes or until the meat is almost cooked to your liking. Transfer from the pan onto a plate and set aside.
Add 1 more tablespoon of oil and let heat. Add the onion and garlic and cook for 1 minute. Add the carrot and broccoli, cook for about 3 minutes then add the bell pepper and cabbage. Cook for another 2-3 minutes or until the vegetables are crisp tender. Add the sauce, cook for 1 minute then add the beef and cook for another 30 seconds or so.