Combine the scotch bonnet peppers, scallions, garlic, ginger, ground allspice, whole allspice berries, thyme, cinnamon, nutmeg, soy sauce, brown sugar, oil, lime juice, salt, and black pepper in a blender or food processor. Blend until a smooth, thick paste forms. Taste carefully — it should be fiery, fragrant, and complex.

Using a sharp knife, score each piece of chicken 2 to 3 times down to the bone. This lets the marinade penetrate deep rather than just coating the surface.

Place the chicken pieces in a large zip-top bag or a glass baking dish. Pour the marinade over the chicken and work it into every cut and crevice with your hands (wear gloves if sensitive to hot peppers). Seal and refrigerate for at least 4 hours, or overnight for best results.

When ready to cook, remove the chicken from the refrigerator 30 minutes before grilling to take the chill off. Preheat a gas or charcoal grill for two-zone cooking: one side on medium-high heat, one side with no direct heat. If using charcoal, add a small handful of soaked wood chips (hickory or allspice wood if you can find it) directly to the coals for extra smoke.

Place the chicken pieces on the indirect-heat side of the grill, skin side up. Close the lid and cook for 30 to 35 minutes, turning once halfway through, until the chicken is mostly cooked through and has taken on color from the smoke.

Move the chicken to the direct-heat side of the grill. Cook for 5 to 8 minutes per side, watching closely, until the skin is deeply charred in spots, blistered, and lacquered-looking. The internal temperature at the thickest part of a thigh should read 165°F on an instant-read thermometer.

Transfer the chicken to a cutting board and let it rest for 5 minutes before serving. Serve on a platter or wrapped in brown butcher paper with rice and peas, roasted plantains, and a lime-dressed slaw alongside.