In a small bowl mix all of the ingredients for the marinade and set aside.
Place the sliced beef in a large bowl, add the marinade and mix to coat the meat well. Cover with plastic wrap and refrigerate for 30 minutes to 1 hour.
In the meantime, mix all of the ingredients for the sauce and set aside.
Uncover the beef and add 3 tbsp of cornstarch. Mix with your hands to coat it well with the cornstarch until it disappears. Set aside.
Parboil the broccoli in boiling water for about 1 minute. Drain and set aside.
Mix 1 tbsp of cornstarch with water and set aside.
Heat oil in a large pan or wok on medium high heat and add the beef. Cook for about 5 minutes or until the beef is almost cooked through. Add the carrots and cook for another 2 minutes. Add the broccoli and cook for another 1-2 minutes or until the broccoli is heated through. Add the sauce and stir well to coat all of the ingredients, then add the dissolved cornstarch and stir for another 30 seconds to 1 minute to let the sauce thicken.
Serve with white rice or noodles.