Marinade: in a small bowl, whisk together the soy sauce, fish sauce palm sugar, lemongrass, garlic, and sesame oil. Place the chicken in a large, resealable plastic food bag and marinate for 1 hour (up to overnight) in the refrigerator.
Preheat broiler. Remove the chicken from the marinade. Broil for 7 minutes per side. transfer to a cutting board and let stand for 5 minutes. Cut the chicken into thin slices.
Dressing: in a small bowl, whisk together the galangal, palm sugar, lime juice, fish sauce, and chili-garlic sauce. Gradually whisk together the ingredients for the Dressing.
Salad: Cook the beans in boiling water until tender-crisp, about 5 minutes. Using a slotted spoon, transfer beans to an ice bath until cool. Drain and set aside.
Combine the reserved beans, coconut, cabbage, peanuts, fresh coriander leaves, mint, basil, onion, and kaffir lime leaves, if using, in a large bowl. Divide the Salad evenly on 4 plates. Divide the chicken pieces evenly among the salads. Drizzle the remaining Dressing on top of the chicken. Serve immediately.
SERVES 4 AS part OF multi-course meal OR FOR lunch