2 10-12-ounce bone-in, skin-on split chicken breasts
6 scallions, white parts coarsely chopped, green parts thinly sliced on a bias, reserved separately
1 1-inch piece fresh ginger, cut into 4 pieces and smashed
2 large garlic cloves, peeled and smashed
1/4 cup dry sherry (optional)
2 tablespoons chili oil
2 tablespoons tahini
1 1/2 tablespoons white sugar
1 1/2 tablespoons toasted sesame oil
1 tablespoon soy sauce
2 tablespoons unseasoned rice vinegar
1 teaspoon Sichuan peppercorns (optional), toasted and finely ground
1/2 teaspoon cayenne pepper
1 large English cucumber, halved lengthwise, seeded and thinly sliced crosswise on a bias
1/3 cup dry-roasted peanuts, chopped
In a large saucepan, place the chicken skin side down, then add the scallion whites, ginger, garlic and 1 1/2 teaspoons salt. Add 4 cups water and the sherry, if using, fully submerging the chicken.
Bring to a boil over medium-high, then cover, reduce to low and cook at a bare simmer until the thickest part of the chicken registers 160°F, 20 to 25 minutes. Uncover the pan and let the chicken cool in the liquid for 15 minutes.
Meanwhile, in a small bowl, whisk together the chili oil, tahini, sugar, sesame oil, soy sauce, vinegar, 1½ teaspoons of salt, Sichuan peppercorns, if using, and cayenne.
Using tongs, remove the chicken from the cooking liquid. Remove and discard the skin and bones, then transfer the meat to a large bowl. Add 2 tablespoons of the tahini dressing, then use a wooden spoon to smash the meat, shredding it and working in the dressing. Use your fingers to pull the shreds into bite-size pieces.
Add the cucumber and ¾ each of the peanuts and scallion greens. Drizzle with the remaining dressing and toss until evenly coated. Transfer to a serving bowl and sprinkle with the remaining peanuts and scallions.