To brine the chicken, slice each chicken breast in half lengthwise, then cut crosswise into halves again, then in a bowl, mix the water and salt until dissolved and add the chicken and brine for 30 minutes, then drain well.
To poach the chicken, in a pot over high heat, bring water to a boil, then reduce to the lowest heat and add the chicken, ginger, and scallions and gently poach for about 15 minutes until the chicken reaches 165°F (74°C), then let cool and shred.
To make the dressing, in a heatproof bowl, combine the sesame seeds, garlic, hot peppers, and chili flakes, then heat the cooking oil until smoking and carefully pour over the aromatics, then add the Chinkiang vinegar and soy sauce and mix well.
To assemble the salad, in a large bowl, combine the chicken, carrot, cucumber, cilantro, peanuts, and dressing and toss until evenly coated.