Boil palm sugar, fish sauce, and coconut milk in a pan.
Simmer chicken thighs in the liquid for 5 minutes until cooked.
Remove chicken, pat dry, and reserve the cooking liquid.
Griddle chicken over high heat for 4 minutes until golden-brown.
Boil the reserved liquid for 2 minutes then cool in an ice bath.
Whisk lime leaves into the cooling coconut milk mixture.
Mix shallots, pepper, chillies, and cucumber in a separate bowl.
Coat the vegetable mixture with one tablespoon of the dressing.
Slice the chicken into strips and add to the salad.
Toss in the herb leaves and mix well.
Brush banana leaves with oil and water mixture on serving plates.
Plate the salad, drizzle with remaining dressing, and top with peanuts and coconut.