How to Make It
In a food processor, combine the garlic, serranos, sugar, coriander, turmeric, curry powder and salt. Pulse to mix. Add the fish sauce and process to a paste, about 30 seconds. Transfer the spice paste to a medium bowl.
Season the chicken with salt and pepper and rub the pieces with 6 tablespoons of the spice paste. Transfer the chicken parts to 4 large, sturdy resealable plastic bags. Whisk the coconut milk into the remaining spice paste in the bowl. Pour the spiced coconut milk into the bags of chicken; gently squeeze out the air in the bags and seal. Turn the bags to coat the chicken thoroughly. Set the bags on a baking sheet and refrigerate overnight.
Preheat the oven to 400°. Remove the chicken from the bags; discard the marinade. Arrange the chicken on 3 large, rimmed baking sheets, skin side up, keeping all of the breast pieces together on the same sheet. Season with salt and pepper. Roast the chicken in batches until browned and an instant-read thermometer inserted in the thickest part of the meat registers 165°, about 25 minutes for white meat; and 35 to 40 minutes for dark meat. If oven space allows, roast two sheets at once: increase the cooking time by 10 minutes for both the white and dark meat. Remove the chicken from the oven and let rest while you roast the rest.
Shortly before serving, light a grill. Grill the chicken skin side down over moderate heat until heated through and the skin is crisp. Transfer the chicken to a platter and serve.