Prep the chicken: Pat the chicken pieces dry.
In a bowl, whisk the egg, soy sauce, and Shaoxing wine. Add chicken and toss to coat. In a separate bowl, mix 1/2 cup cornstarch, flour, salt, and pepper.
Dredge the egg-coated chicken in the dry mixture until each piece is well covered. Set aside while you heat the oil.
Mix the sauce: In a measuring cup, whisk soy sauce, rice vinegar, sugar, hoisin, water or broth, and 2 teaspoons cornstarch until smooth. Set near the stove.
Heat the oil: In a deep skillet or wok, add 1 to 1.5 inches of oil.
Heat to about 350–365°F. If you don’t have a thermometer, drop in a small bit of coating—it should sizzle quickly and rise to the top.
Fry the chicken (first fry): Fry in batches without crowding, 3–4 minutes, until lightly golden and just cooked. Transfer to a wire rack or paper towel–lined tray.
Fry again (second fry): Increase oil heat slightly to maintain 360–370°F.
Fry the chicken a second time for 1–2 minutes until deep golden and very crisp. Drain and set aside. This step locks in crunch.
Stir-fry aromatics: Pour off the oil, leaving 1 tablespoon in the pan.
Add dried chilies (or crushed red pepper), garlic, ginger, and the white parts of the scallions. Stir-fry 30–45 seconds until fragrant but not browned.
Thicken the sauce: Stir the sauce again (cornstarch settles), then pour into the pan. Cook over medium heat, stirring, until glossy and thick, about 1–2 minutes.
Add sesame oil for a nutty finish.
Combine: Add the fried chicken to the pan and toss quickly to coat every piece. If sauce seems too thick, splash in a tablespoon of water to loosen. Turn off the heat.
Garnish with green scallion tops and sesame seeds.
Serve: Plate over hot steamed rice with broccoli on the side. Eat immediately for peak crispiness.