Crush the peppercorns and coriander in a mortar. Add the palm sugar and garlic and mash together. Transfer to a saucepan and add the turmeric, fish sauce, chile powder, vegetable oil and 2 tablespoons water. Cook over medium-low heat until the sugar is melted. Let cool to room temperature.
Once cooled, pour the marinade into a large bowl and add the chicken quarters. Rub the marinade all over chicken and refrigerate 8 hours or overnight.
Preheat the oven to 400 degrees F. Place a rack in a roasting pan or on a rimmed baking sheet. Put the chicken on the rack and roast for 25 minutes. Lower the oven temperature to 350 degrees F and roast until the skin is brown and crispy and the chicken is cooked through, about 30 minutes more.
Remove the chicken from the oven and let rest 5 to 10 minutes. Serve with sticky rice and papaya salad.
It's important to let the marinade soak into the chicken overnight so you get juicy meat with crispy skin. This dish is best served with papaya salad so you can soak the chicken and rice with the dressing from the papaya salad.