Position a rack in the middle of the oven and preheat to 450 degrees.
Rub the chicken with the sesame oil, salt and pepper. Gently slide your finger underneath the skin of each breast to loosen it from the meat; this will encourage the skin to crisp as it cooks. Place the chicken on a large, rimmed baking sheet, skin side up. Roast for 30 to 35 minutes, or until the skin is browned and crisp and an instant-read thermometer inserted into the thickest part of a breast reads 160 degrees.
While the chicken is roasting, make the sauce and prepare the garnishes. In a small bowl, stir together the soy sauce, vinegar, sugar, chile crisp or oil, sesame paste, if using, sesame oil and ginger.
To prepare the garnishes, julienne the cucumbers, roughly chop the peanuts, if using, thinly slice the scallions on a bias and coarsely chop the cilantro.
Let the cooked chicken cool for about 10 minutes. Using a rolling pin, gently bang or press down on each chicken piece so the meat breaks and shreds apart a bit. Pull the chicken fully away from the bones, and, if preferred, remove and discard the bones. The chicken should be in chunks and shredded bite-size pieces. Serve the chicken over rice, noodles or shredded lettuce with the cucumbers, peanuts, if using, scallions and cilantro sprinkled on top. Scrape any pan drippings into the sauce. Serve it on the side to drizzle generously over each serving.