Marinate chicken cubes in 1 tablespoon Shaoxing wine and ½ teaspoon salt.
Heat wok until hot and add 3 tablespoons peanut or canola oil. When oil is hot, turn heat to low, add nuts and gently stir-fry until toasty brown all over. Watch closely so they don't burn. Remove from wok and let drain on paper towel. They will firm up and become crunchy when cool. (Don't be tempted to substitute roasted nuts or skip this step; it makes all the difference.)
Mix sauce ingredients together in a measuring cup: Zhenjiang vinegar, chicken stock, light soy sauce, sugar, 1 tablespoon Shaoxing wine, cornstarch, and 1 teaspoon salt.
Clean wok and heat over a high flame until extremely hot (which keeps the chicken from sticking). Add 2 tablespoons oil, swirl around the pan and add the chicken cubes. Spread the chicken out around the wok, and let the pieces sear on one side. Flip the chicken and let sear on the other side. Stir-fry until chicken is cooked through and lightly browned. Remove chicken from wok and let drain on a paper towel.
Clean work and return to heat. When wok is hot, add 3 tablespoons fresh oil and heat briefly on a medium flame. Add chili peppers and Sichuan peppercorns and stir-fry vigorously, toasting but not burning them. Add the scallion whites, ginger and garlic and stir-fry until fragrant.
Add back the chicken cubes and toss in the scallion greens. Stir-fry briefly and mix well. Add the sauce and mix well. As the sauce thickens, add back the cashew nuts and stir-fry briefly until all ingredients are well combined. Plate and serve.