Thinly slice the beef into strips a few inches long and about 1/4-inch wide. Toss with egg in a medium bowl. Stir together the cornstarch and water and add to the beef; toss to blend well.
In a small bowl or measuring cup, stir together the sugar, soy sauce, vinegar, wine, sesame oil and chili flakes. Stir in half the ginger and garlic.
In a wok or heavy pot, heat about an inch of oil over medium-high heat until hot but not smoking. Drop the strips of beef into the oil using a fork, chopsticks or tongs, keeping them from clumping together and cooking in batches so the beef doesn't crowd the pot. Once golden and crisp, transfer to a paper towel-lined plate or sheet. Pour the oil out into a jar (or start with a fresh pan or wok with a new drizzle of oil) and add the pepper, carrots, green onion and remaining ginger and garlic to the pan. Cook for a minute or two, then pour the sauce overtop and heat through. Put the beef in a shallow bowl, pour the sauce over top and serve immediately.
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