Place chicken breast, ginger slices, scallion segments, and Shaoxing wine in a pot and cover with water.
Bring to a boil, then reduce heat to low and simmer for 12 minutes or until the internal temperature reaches 74C (165F).
Remove chicken from the pot and immediately submerge in ice water to stop the cooking process.
Once cooled, use a rolling pin to lightly pound the chicken breast to loosen the muscle fibers.
Shred the chicken by hand into thin, uniform strips.
Arrange julienned cucumber on a serving platter as a base and layer the shredded chicken on top.
In a mixing bowl, whisk together sesame paste, light soy sauce, black vinegar, sugar, chili oil, Sichuan pepper powder, minced garlic, and minced ginger until smooth.
Drizzle the sauce evenly over the chicken and garnish with toasted sesame seeds and chopped scallions.