01 - Rinse chicken pieces with lime juice and vinegar, then rinse thoroughly under cold water and pat dry with paper towels.
02 - Combine salt, black pepper, all-purpose seasoning, browning sauce, garlic, thyme, scallions, Scotch bonnet, onion, and paprika. Massage the marinade evenly into the chicken, cover, and refrigerate for at least 1 hour or overnight for best results.
03 - Heat vegetable oil in a large heavy pot or Dutch oven over medium-high heat. Shake off excess marinade from the chicken and reserve it. Sear the pieces in batches until deeply browned on all sides, about 6 to 8 minutes per batch.
04 - Remove the browned chicken and set aside. Add the bell pepper, carrots, and tomato to the same pot and sauté for 2 to 3 minutes until slightly softened.
05 - Return the chicken to the pot along with the reserved marinade, ketchup, chicken broth, and soy sauce. Stir to combine, bring to a simmer, then cover and reduce heat to low. Cook for 45 to 55 minutes, stirring occasionally, until the chicken is fork-tender and the sauce has thickened.
06 - Taste and adjust seasoning as needed. Discard the thyme stems before serving.