Prepare finishing sauce by combining all the ingredients in a small bowl. Set aside.
Cut the flank steak extremely thin and place in a bowl. Mix together the corn starch and rice wine and pour over the steak pieces. Stir well to coat all the meat. Marinate the meat for about 15 minutes.
While the steak is marinating, steam the broccoli just until it turns bright green. Remove the broccoli from the steamer. Do not cook it all the way to tender; it will finish cooking while it is stir-fried.
Heat wok or large skillet until it is hot. Pour in oil and swirl it around. Lay out meat in one layer and let it cook until browned. Turn over the beef slices, add the garlic and ginger, and mix around quickly. Add the broccoli. Give the finishing sauce a quick stir and pour it over the beef and broccoli. Stir everything together until the sauce thickens. Serve over rice.