In a bowl, combine the chicken pieces with Shaoxing wine, water, salt, white pepper, and sesame oil. Stir thoroughly until the liquid is fully absorbed. Sprinkle in the toasted sesame seeds, followed by the all-purpose flour and cornstarch, ensuring each piece is evenly coated. Set aside.

Prepare the sauce by whisking together the chicken stock, dark soy sauce, soy sauce, brown sugar, and rice wine vinegar in a small bowl. Set aside for later use.

Bring a pot of water to a rolling boil. Blanch the broccoli for 30 to 60 seconds, depending on the preferred texture. Drain immediately and set aside. For enhanced color and crispness, transfer the broccoli to an ice bath before draining.

In a small, deep pot, heat the frying oil to 335°F (170°C). Carefully lower the coated chicken pieces into the oil in small batches, ensuring they are evenly battered. Fry for approximately 5 minutes, or until the pieces turn a light golden brown and begin to float. Remove from the oil and transfer to a wire rack or a plate lined with paper towels to drain.

Monitor the oil temperature throughout the process, reheating as necessary between batches. Once all the chicken has undergone its initial frying, return it to the oil for a second round, frying for an additional 3 to 5 minutes to achieve a deep golden crisp. Take care not to overcook.

Heat a clean wok over medium heat, adding a tablespoon of oil. Toss in the dried chili peppers, stirring for a few seconds until aromatic. Add the minced garlic and Shaoxing wine, allowing the flavors to meld.

Pour in the prepared sauce, bringing it to a gentle simmer. Gradually introduce the cornstarch slurry, stirring continuously until the mixture thickens and takes on a glossy sheen. Return the crispy fried chicken to the wok, along with the blanched broccoli. Toss everything together until evenly coated with the sauce.

Serve immediately, accompanied by steamed rice for a well-rounded and satisfying meal.