Prep the vegetables. Core the cabbage and slice it as thinly as you can.
Slice the cucumber and bell pepper, shred the carrots, and chop the scallions and herbs. Keep everything roughly the same size for an even bite.
Shred the chicken. Use two forks to pull cooked chicken into bite-size pieces. Warm or cold both work.
If using rotisserie, remove the skin for a lighter salad.
Make the dressing. In a small bowl, whisk rice vinegar, soy sauce, sesame oil, neutral oil, honey, lime juice, ginger, garlic, and sriracha. Taste and adjust with a pinch of salt, pepper, or an extra squeeze of lime.
Combine the salad. In a large bowl, add both cabbages, carrots, cucumber, bell pepper, scallions, and chicken. Pour in about two-thirds of the dressing and toss well.
Adjust and finish. Add more dressing as needed to lightly coat everything without pooling at the bottom.
Fold in cilantro (and/or mint) and most of the nuts and sesame seeds.
Serve with crunch. Top with remaining nuts and sesame seeds for extra texture. Taste one more time and add a sprinkle of salt, a crack of pepper, or a few drops of lime if needed.