Cut tops of green onions into 2" long pieces. Combine sauce ingredients in small bowl and stir thoroughly. Cut steak across the grain into thin slices, about 1/2" deep by 2" long.
In bowl big enough to hold meat, combine egg whites, salt and water chestnut flour. Beat with chopstick until frothy. Add steak, and use fingers to coat each slice.
Deep-frying: In wok, heat oil to moderately hot. When ready, piece of coated meat will rise to surface immediately. Fry meat in small batches; drop in 1 slice at a time to avoid sticking. Cook until lightly brown, about 1 minute. Drain on Chinese strainer or paper bag.
Stir-frying: Remove all but 2 T of oil from wok. With wok at medium heat, quickly stir-fry green onions and ginger for about 20 seconds. Add sauce; bring to boil on high heat while stirring. Add beef all at once, and toss with sauce until beef is hot and coated. Push beef out of sauce, dribble in cornstarch paste to lightly thicken. Recombine.