Prepare the chicken. Remove the skin if desired and trim away excess fat. Do not wash raw chicken; instead, pat the pieces thoroughly dry with paper towels. Cut the chicken into manageable pieces.
Marinate the chicken. Place the chicken in a large bowl or food-safe storage bag. Add the onion, green onion, garlic, thyme, bay leaves, browning sauce, Scotch bonnet, black pepper, paprika, allspice, brown sugar, ginger, salt, bell peppers, and soy sauce if using. Toss thoroughly so every piece is well coated.
Rest the marinade. Cover and refrigerate for at least 1 hour. For deeper flavor, marinate overnight.
Brown the chicken. Heat the olive oil in a large Dutch oven or heavy-bottomed skillet over medium-high heat. Remove the chicken from the marinade, allowing excess liquid to drip off. Reserve the marinade. Brown the chicken in batches if necessary, cooking each side until deeply golden, about 5–10 minutes total.
Build the stew. Return all the browned chicken to the pot. Pour in the chicken stock and add the reserved marinade. Stir gently and bring the mixture to a boil.
Simmer. Reduce the heat slightly, cover the pot, and simmer for about 20 minutes, allowing the chicken to cook through and absorb the seasoned broth.
Add the ketchup. Remove the lid and stir in the ketchup. Reduce the heat to medium-low.
Reduce the sauce. Cover again and continue simmering for approximately 10–15 minutes, or until the chicken is tender and the sauce has reduced to a rich, flavorful consistency.
Finish and serve. Taste and adjust the salt and black pepper. Remove the bay leaves, thyme stems, and whole Scotch bonnet pepper if used. Serve hot with your favorite side dishes.