In a large bowl, combine the soy sauce, vinegar, 2 tablespoons of the sugar and the egg whites. Stir until the sugar dissolves. Add the chicken and stir to coat, then cover and let marinate at room temperature for 20 to 30 minutes.

In a large bowl, whisk together the cornstarch, ground Sichuan peppercorns and 1 teaspoon salt. Working in batches, remove the chicken from the marinade, allowing any excess to drip off, and coat evenly in the cornstarch mixture, pressing gently to adhere. Transfer the coated chicken pieces to a wire rack set in a rimmed baking sheet.

In a large Dutch oven or heavy-bottomed pot, add enough vegetable oil to measure about 2 inches deep and heat over medium-high until it registers 375°F on an instant-read thermometer. Working in batches, add the coated chicken pieces to the hot oil and fry until golden brown and crispy, about 4 minutes per batch. Transfer the fried chicken to a second wire rack set in a rimmed baking sheet.

In a small saucepan, heat the Sichuan chili oil and chili flakes over medium until sizzling; cook for 2 minutes. Stir in the sesame oil, garlic and ginger, then cook until fragrant, about 1 minute. Remove from the heat and stir in the remaining 1 tablespoon sugar.

Pour the chili sauce over the fried chicken and toss to coat. Transfer to a serving platter, sprinkle with the sliced green onions and reserved dark green onion tops, and serve.