Place the chicken pieces in a wide pan or Dutch oven. Pour in the thin coconut milk and cook over medium heat until the chicken turns opaque and is about halfway cooked. Keep the heat gentle to prevent the coconut milk from boiling aggressively.
Add the blended spice paste (and kaffir lime leaves, if using). Stir gently to coat the chicken evenly. Pour in the thick coconut milk, reduce the heat to low, and simmer uncovered.
Cook slowly, stirring occasionally, until the coconut milk reduces significantly and releases its natural oil. The sauce should look thick, glossy, and aromatic—not watery.
Add the toasted grated coconut and optional palm sugar. Stir well until the mixture becomes dry and clings tightly to the chicken. Taste and adjust seasoning if needed.
Remove the chicken from the pan. Press each piece between two bamboo skewers or secure with metal skewers.
Grill over medium heat (outdoor grill, grill pan, or oven broiler) until lightly charred and fragrant, about 2–3 minutes per side. Brush with any remaining coconut mixture for extra flavor.
Serve hot with steamed rice and a simple chili sambal or fresh salad.