Whisk the peanut butter and warm water in a medium bowl until smooth.
Add the soy sauce, lime juice, rice vinegar, honey, sesame oil, garlic, and ginger to the bowl.
Whisk until the dressing is emulsified and pourable. Add an extra tablespoon of water if too thick.
Poach the chicken breasts in salted water until they reach 165F (15-20 minutes).
Shred the warm chicken using two forks.
Spread the shredded chicken on a plate and refrigerate for 2 hours until cold.
While the chicken cools, prep all the vegetables, herbs, and peanuts.
Cut the mango and cucumber into thin, uniform matchsticks.
In a large bowl, combine the cold chicken, cabbages, carrots, cucumber, mango, bell pepper, scallions, and herbs.
Pour three-quarters of the dressing over the salad and toss with tongs.
Add the chopped peanuts and toss again.
Taste and add remaining dressing if needed.