In a 5 quart saute pan, add your coconut oil. Set over medium heat and add ½ your curry paste. Cook for about 2 minutes, stirring often, until the paste starts to stick to the bottom of the pan and become very fragrant. At this stage, add your coconut milk, increase the heat to medium high, and bring to a boil
Once boiling, add in your water, black soy sauce, soy sauce, and palm sugar. Stir and bring to a boil then immediately reduce the heat to low and simmer. Lower in your chicken drumsticks, bring back to a simmer, and cover with a lid. Let the chicken poach in the broth for 40 minutes or until the drumsticks are cooked through and tender.
Once done, add your fish sauce and lime juice. Taste and adjust with fish sauce, lime juice, and palm sugar until the flavor is to your liking.