Bring the water or stock to the boil in a large saucepan over a high flame. Add the chicken and return the liquid to a boil, skimming the surface as necessary.
Crush half the ginger and one scallion with the flat side of a cleaver or a heavy object, then add to the pan with the chicken. Reduce the heat and poach the chicken for 10 minutes.
Remove the chicken from the cooking liquid and allow it to cool; reserve the cooking liquid. The chicken should be about three-quarters cooked.
When the chicken is cool enough to handle, remove the flesh from the carcass and cut as far as possible into bite-size strips, along the grain of the meat. Do not discard the skin. (The bones and scrappy pieces of meat can be returned to the cooking liquid and made into stock.).
Cut the fresh chile in half lengthwise and discard the seeds and pithy part, then cut into very fine slivers about 1 1/2 inches long. Peel the remaining ginger and cut it into slices and then slivers similar to the chile. Cut the green parts of the remaining 2 scallions into slivers of a similar length; set aside.
Heat the wok over a high flame until smoke rises, then add the lard or peanut oil and swirl around. When the oil is warming up but before it is smoking hot, add the fresh chile and ginger, along with the dried chiles and Sichuan pepper (if using), and stir-fry until fragrant, taking care that the seasonings do not take color or burn.
Add the chicken and continue to stir-fry. Splash the Shaoxing wine around the edges of the chicken. Add the vinegar, Sichuan pepper oil (if using), and salt to taste.
Add up to a cup of the chicken poaching liquid (if the chicken is very juicy, no additional liquid will be necessary), bring to a boil, and then turn the heat down a little and simmer briefly to allow the flavors to penetrate the chicken, spooning the liquid over.
Add the potato flour mixture to the liquid and stir as the sauce thickens. Throw in the scallion greens and stir a few times. Remove from the heat and stir in the sesame oil. Serve.