Trim any excess fat from the oxtail. Rinse with water and vinegar, rubbing the pieces to remove any dried blood, bone fragments, or debris.

Add the oxtail to a large bowl with the green seasoning, Worcestershire sauce, and fresh thyme. Mix well to coat. Marinate for at least 30 minutes or overnight. If marinating overnight, remove the oxtail from the refrigerator about 30 minutes before cooking.

Heat the oil in a large, heavy-bottomed pot over medium-high heat. Add the brown sugar to the center of the pot and allow it to caramelize until dark brown and bubbling.

Add the seasoned oxtail to the caramelized sugar and mix well to coat the pieces. Continue cooking and stirring until the liquid released from the meat has mostly evaporated.

Add enough water to come just above the oxtail and bring to a boil. Add the bay leaves, lower the heat to medium, and simmer for about 1 hour, checking the liquid level occasionally.

After 1 hour, add the whole hot pepper. Taste the gravy and add 1 teaspoon all-purpose seasoning, along with salt and black pepper as needed.

Continue simmering until the oxtail is tender, about another hour. If the liquid gets too low while the meat is still tough, add enough water to come about halfway up the oxtail and continue cooking.

Add the carrots and ketchup or tomato paste toward the end of cooking. Continue simmering until the carrots are tender and the oxtail is cooked to your liking.

If needed, add a little more water for gravy. Simmer uncovered over low heat until the gravy reduces and thickens.