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Place cornstarch in a large bowl. Add water gradually while whisking. Beat eggs into cornstarch mixture.
Toss in beef and stir to coat.
Pour 1 inch of oil into wok, heat until boiling hot, but not smoking.
Add a quarter of the beef to the oil. Separate with a fork and cook, stirring frequently, until crispy. Remove, drain on paper towel and set aside. Repeat until all the beef is cooked.
Drain off all oil except for about 1 tablespoon and add carrots, onion, ginger, and garlic in that order. Stir fry briefly over high heat.
Combine last 5 ingredients and add to vegetable mixture. Bring to a boil and then add beef. Heat through and serve immediately, with chow mein.