Slice beef very thin, approximately 1/4 to 3/8 inches thick. Place meat between sheets of plastic wrap and use a meat tenderizer and gently pound meat into uniform pieces. If you are using skirt steak cut the meat diagonally, it will help make the meat more tender.
Place cornstarch in a bowl and dip steak pieces into cornstarch and shake off excess cornstarch. Allow the cornstarch dipped pieces of meat to rest for 5 to 10 minutes so the coating sticks to the meat. While the meat is resting you can continue to prep the remaining ingredients.
In a wok, heat wok oil (vegetable oil is ok to use). Place beef in a single layer in the pan. Saute beef until just done, and the outside begins to crisp. Remove meat from pan. You may need to do this a few pieces at a time.
Once all of the meat has been cooked and removed from the pan, add minced ginger and garlic. Saute ginger and garlic for approximately 60 seconds, the remaining oil should become very fragrant.
Mongolian Beef Sauce
In a small bowl combine soy sauce, water, red pepper flakes, brown sugar, and rice wine vinegar. Stir well. Add the sauce to the pan until the sauce thickens, return meat to pan, and add sliced button mushrooms to the pan.
Finishing the dish
Cook for another 60 seconds or so and chopped green onion white portions only, and add half of the green options. When serving the Mongolian beef add remaining green onion slices to the dish.