Make the jerk seasoning: Place the ingredients for the seasoning in a food processor or blender. Pulse for 10 seconds, until the mixture is combined but not totally smooth. Set aside ¼ cup of the marinade, then transfer the rest to a large glass or ceramic dish or resealable plastic bag. Place the ¼ cup of marinade in the fridge.
Marinate the chicken: Pat the drumsticks dry, season them with a pinch of salt, and add them to the dish or plastic bag with the jerk seasoning. Mix to coat the chicken evenly, then marinate in the refrigerator for a minimum of 4 hours or up to 24 hours.
Thirty minutes before you’re ready to cook the chicken, remove the chicken from the marinade and allow it to come to room temperature. Preheat a grill to medium heat. Meanwhile, prepare the rice and salsa.
Combine the ingredients for the salsa in a bowl and set aside.
Make the Caribbean rice: In a skillet that has a lid, melt the butter over medium heat. Add the ginger and garlic and sauté until fragrant, about 1 minute.
Add the rice and stir until all of the rice is coated in the butter, about 1 minute, then add the water, coconut milk, salt, pepper, and lime zest. Bring to a boil over medium heat, then reduce the heat to low and cover. Cook for 40 minutes, or until the rice is fluffy.
While the rice is cooking, grill the chicken: Brush the hot grill grate with oil. Place the chicken on the grill and cook for 8 minutes, then flip, brush with the reserved marinade, and grill for an additional 8 minutes. Turn the chicken over one last time, brush again with the remaining marinade, and cook for 5 more minutes, or until no pink remains in the center of the chicken.
To serve: Place the rice on plates, then add the chicken, mango salsa, and sliced avocado.