Slice steak across the grain into narrow strips.
Place cornstarch in a large mixing bowl. Add water gradually while you are whisking. Beat eggs into cornstarch mixture. Toss in beef and stir to coat.
Pour 1 inch of oil into wok, heat to boiling hot, but not smoking. Add a quarter of the beef to the oil at a time. Separate with a fork and cook, stirring frequently, until crispy. Remove, drain on parchment and set aside. (This much can be done in advance.)
Put oil in wok. Add carrots, bell pepper, onion, ginger and garlic in that order. Stir briefly over high heat.
Combine soy sauce, wine, vinegar, sesame oil, sugar and chili flakes. Add to vegetable mixture and bring to a boil.
Add beef, mix well. Serve over rice!