In a large bowl, whisk together soy sauce, olive oil, brown sugar, lime juice, minced garlic, grated ginger, fresh thyme leaves, ground allspice, black pepper, paprika, cinnamon, nutmeg, cayenne pepper, and salt to create the jerk marinade.

Place the chicken thighs and drumsticks in a large resealable plastic bag or shallow dish. Pour the jerk marinade over the chicken, ensuring each piece is well coated. Seal the bag or cover the dish and refrigerate for at least 4 hours, or preferably overnight, to allow the flavors to penetrate the meat.

Preheat your grill to medium-high heat (around 375-400°F/190-200°C). If using charcoal, set up a two-zone fire with the coals on one side for direct heat and the other side for indirect heat.

Remove the marinated chicken from the refrigerator and let it sit at room temperature for about 30 minutes before grilling.

Once the grill is hot, lightly oil the grates to prevent sticking. Remove the chicken from the marinade, shaking off any excess, and place it on the grill over direct heat, skin side down.

Grill the chicken for about 5-7 minutes per side, or until the skin is crispy and golden brown, and the internal temperature reaches 165°F (74°C) for thighs and drumsticks. Rotate the chicken occasionally to ensure even cooking and to prevent burning.

Once the chicken is cooked through, transfer it to the cooler side of the grill (indirect heat) and continue to cook for an additional 10-15 minutes, allowing it to absorb the smoky flavor from the grill and ensuring it's fully cooked.

Remove the grilled jerk chicken from the grill and let it rest for a few minutes before serving. Garnish with lime wedges and fresh thyme sprigs for an extra burst of flavor.

Serve your Jamaican jerk chicken hot alongside traditional sides like rice and peas, fried plantains, or fresh salad, and enjoy the bold, spicy flavors of this classic Caribbean dish!