Whisk soy sauce, garlic, brown sugar, tahini, sesame oil, rice vinegar, ginger, sriracha, and sesame seeds in a bowl.
Add the chicken breast, turn to coat, cover, and marinate for at least 20 minutes or up to 8 hours.
Cook the chicken in a skillet over medium heat until browned and the thickest part reaches 165°F.
Rest the chicken for 5 minutes, then slice it into thin strips.
Whisk peanut butter, rice vinegar, honey, sesame oil, soy sauce, ginger, garlic, sriracha, and warm water until smooth.
Combine purple cabbage, green cabbage, carrot, bell pepper, edamame, green onion, cilantro, and peanuts in a large bowl.
Toss the slaw with dressing, top with sliced chicken, and finish with extra peanuts if desired.