In a bowl, whisk together the egg white, 2 tablespoons of the cornstarch, 2 tablespoons of the wine, and 1 tablespoon of soy sauce. Add the chicken and toss to coat. Cover and marinate in the refrigerator for up to 2 hours.
To make the sauce, in another bowl, whisk remaining 1 tablespoon cornstarch with 1 tablespoon of the chicken stock until smooth. Add the remaining 3 tablespoons chicken stock, 1 tablespoon wine, 1 tablespoon soy sauce, the vinegar, and sugar and whisk to combine. Set aside until ready to finish the dish.
In a large wok or pot, heat enough oil to come 3 inches up the sides to 350 degrees F.
Remove the chicken from the marinade and carefully slide into the hot oil. Fry, turning, until golden brown and cooked through, about 2 minutes. Remove and drain on paper towels.
Discard all but about 1 tablespoon of the oil from the wok. (Alternatively, in a clean wok or saute pan, heat 1 tablespoon of oil over medium-high heat.) Add the chile peppers and stir-fry until nearly black. Add the garlic, ginger, red pepper flakes and 1/2 cup green onions. Stir-fry until fragrant, about 15 seconds. Add the chicken stock sauce, bring to a boil, and cook, stirring, until the sauce thickens, about 1 minute. Remove from the heat.
Arrange the chicken on a platter and pour the sauce over it. Garnish with the cashews and additional green onions. Serve with hot rice.