Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Beat the eggs in a mixing bowl until smooth. Stir in 1/2 cup of cornstarch until no lumps remain, then mix in the chicken until evenly coated in batter.
In batches, carefully drop the chicken cubes into the hot oil one by one, cooking until the chicken turns golden brown and begins to float, about 3 minutes. Drain on a paper towel-lined plate.
Heat the vegetable oil in a wok or large skillet over high heat. Stir in the dried peppers, and cook for about 30 seconds until the color brightens. Add the chicken, and cook for a few minutes until the chicken turns a deep, golden brown. Stir the vinegar, rice wine, sugar, soy sauce, and 2 teaspoons of cornstarch together in a small bowl. Pour into the wok, and boil until the sauce thickens and is no longer cloudy, about 2 minutes. Garnish with green onions to serve.
