Combine peppers, scallions, ginger, garlic, thyme, allspice, nutmeg, brown sugar, soy sauce, lime zest and juice, olive oil, 2 teaspoons black pepper, and 1 tablespoon kosher salt in the work bowl of a food processor or the jar of a blender. Blend until a rough purée is formed, about 1 minute.
Divide chicken and marinade between two gallon-sized zipper-lock bags, or place in a large baking dish and cover tightly with plastic wrap. Place whole allspice berries and bay leaves in a gallon-sized zipper-lock bag and fill with water. Refrigerate chicken and bay leaves at least 10 hours and up to 1 day.
When ready to cook, remove chicken from bags, allow excess marinade to drip off, and transfer to a large plate. Light one half chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and pile the coals against one wall of a kettle grill. Alternatively, set the leftmost burners of a gas grill to medium-high heat. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Clean and oil the grilling grate. Set bottom and lid vents to half-open. Lay the chickens on the grill skin side up with the legs pointed towards the hotter side of the grill and immediately cover, with the vent above the chicken. Cook for 15 minutes.
Open lid, add 15 new coals (if necessary) to the pile of hot coals. Cover and continue to cook until the internal temperature of the chicken registers 145°F (63°C) on an instant-read thermometer, about 20 minutes longer.
Uncover grill and wait 5 minutes until coals are hot again (if using gas grill, increase heat to high). Carefully transfer chicken to the hot side of the grill skin side up. Cook the chicken until lightly charred, about 3 minutes. Flip chicken and continue to cook until skin is crisp and charred and coolest part of breast registers 150°F to 155°F (66°C to 68°C) on an instant-read thermometer, 4 to 6 minutes longer.
During the last 5 minutes, brush with Tropical Mango Sauce, flipping and basting again.
Remove from grill, transfer to a large platter, allow rest for 5 minutes, and garnish with cilantro.
Reserve more sauce for dipping!
Serve with grilled pineapple or any of your favorite sides.