Make the dressing: In a bowl, whisk peanut butter, soy sauce, rice vinegar, lime juice, honey, sesame oil, sriracha, garlic, and ginger. Add warm water a tablespoon at a time until the dressing is smooth and pourable, like heavy cream.
Taste and adjust with more lime or soy as needed.
Prep the veggies: Shred the cabbages, julienne the carrot, slice the bell pepper and cucumber, and chop the herbs. Keep the pieces bite-sized for easy eating and even distribution.
Combine the base: In a large mixing bowl, add the cabbages, carrots, bell pepper, cucumber, green onions, cilantro, and mint or Thai basil if using. Toss gently to combine.
Add the chicken: Fold in the shredded chicken so it’s evenly distributed.
If the chicken is cold from the fridge, let it sit out for a few minutes so it doesn’t seize the dressing.
Dress the salad: Pour about two-thirds of the peanut dressing over the salad. Toss well to coat. Add more dressing as needed so everything is lightly but thoroughly coated, not drenched.
Finish with crunch: Top with chopped peanuts and sesame seeds.
Serve with lime wedges for squeezing over the top. A final squeeze of lime brightens all the flavors.
Optional chill: For an extra-refreshing salad, chill it for 15–20 minutes before serving. Add the peanuts right before eating so they stay crunchy.