Remove backbone from leg quarters using a paring knife. Split into drumstick and thigh along the joint to create 8 pieces.
Mix salt and sugar. Season both sides of chicken generously. Chill uncovered in fridge for 15–20 minutes.
In a food processor, combine thyme, garlic, scallions, ginger, habanero, olive oil, soy sauce, brown sugar, allspice, cinnamon, nutmeg, and lime juice. Blend until mostly smooth but still slightly textured.
Toss the brined chicken with half the marinade. Arrange skin-side up on a sheet tray. Brush any exposed areas with extra marinade. Chill uncovered for at least 4 hours, preferably 24.
Set up for 2-zone cooking. Add wood chips (preferably pimento or hickory) to a smoker box or foil pouch on the hot side. Preheat grill to about 300°F with good smoke flow.
Oil the grates well. Place chicken skin-side down on the cooler side. Grill for 10 minutes. Flip, brush grilled side with more marinade, and cook another 10 minutes. From this point on, flip the chicken every 5-10 minutes until deep browning has occurred and the internal temperature hits 185℉. Be sure to brush more marinade on after each flip. When the process is done, the skin should be rendered and slightly crisp.
Make sauce (optional): Simmer remaining marinade with water over med heat for 5 minutes. Blend until smooth.
Let the chicken rest for 10 minutes. Serve hot, optionally with a drizzle of jerk sauce and a squeeze of lime.