Salt the chicken breasts all over, place in a bowl, cover with plastic wrap and refrigerate for at least 30 minutes and up to 8 hours.
When you’re ready to poach the chicken, place the wine, scallions, ginger, garlic and 1½ quarts water (or or more if needed to submerge the chicken) in a pot. Bring to a boil, add the chicken, bring back to a boil and cook for 2 minutes. Cover and turn off the heat. Let the pot sit until the chicken is opaque and cooked through (an instant-read thermometer stuck into the thickest part should read 165ºF), 12 to 15 minutes.
While the chicken is cooking, prepare a salted ice bath. Whisk 2 tablespoons salt with 2 quarts water, then add enough ice to create a chilly bath; this will shock the chicken to stop it from cooking and quickly chill the meat so you can shred it easily.
When the chicken is done, transfer it to the ice bath and swish around with tongs. Once cool, transfer to a board or plate (let any excess water drip off) and shred into thin, long pieces along the grain (as you would with pulled pork).
Discard the ice water and dry the bowl thoroughly. Add all the dressing ingredients to the bowl and whisk well to thoroughly combine. Add the shredded chicken, toss it in the dressing to coat, then add the cucumber, celery, cilantro and sesame seeds. Toss gently to combine.
Place the lettuce leaf cups on serving plates and top with the chicken salad. Drizzle with chili crisp or chili oil, if desired, and serve.