In a blender or food processor, combine scallions, thyme, garlic, onion, Scotch bonnet peppers, salt, allspice, black pepper, browning seasoning, soy sauce, brown sugar, lime juice, liquid smoke (if using), and oil. Blend until smooth to create the marinade.
Reserve 4 tablespoons of marinade (2 tbsp for the rice and 2 tbsp for the gravy), and pour the rest over the chicken quarters in a large bowl or ziplock bag. Coat the chicken thoroughly and let it marinate in the fridge for at least 8 hours or overnight for best flavor.
Preheat your grill or oven to 375°F (190°C). Remove the chicken from the marinade and shake off excess. Grill or bake the chicken for 45–60 minutes, turning occasionally, until the skin is charred in spots and the internal temperature reaches 165°F (74°C).
While the chicken is cooking, prepare the rice. In a large pot, combine the brown rice, chicken stock, coconut milk, 2 tbsp reserved jerk marinade, and red beans. Bring to a boil, then reduce to a simmer, cover, and cook for about 40–45 minutes, or until rice is tender and liquid is absorbed.
For the jerk gravy, combine the remaining 2 tbsp jerk marinade, soy sauce, Worcestershire sauce, and water in a small saucepan. Bring to a simmer. In a small bowl, mix cornstarch with a tablespoon of water to make a slurry, then stir it into the gravy. Simmer until thickened.
Serve the grilled jerk chicken over the coconut rice and beans, and drizzle with the spicy jerk gravy. Garnish with lime wedges or fresh herbs if desired.