Prepare the oxtail: Remove all bones and hard cartilage from the cooked oxtail. Trim excess solid fat and cut or pull the meat into bite-size pieces. Measure 2 tablespoons of reserved oxtail gravy and set aside.
Scramble the eggs: Heat a large wok or heavy skillet over medium-high heat. Add 1 teaspoon of oil. Pour in the beaten eggs and stir gently until just set. Transfer the eggs to a plate and set aside.
Crisp the oxtail: Add 1 tablespoon of oil to the hot skillet. Spread the cooked oxtail in a single layer and leave it undisturbed for 30 to 45 seconds. Toss and cook for another 2 to 3 minutes, until the edges are browned and lightly crisp. Transfer the oxtail to a plate.
Cook the vegetables: Add the remaining oil to the skillet. Add the onion, carrots, and red bell pepper. Stir-fry for 2 to 3 minutes. Add the garlic, ginger, thyme, allspice, white parts of the scallions, and Scotch bonnet if using. Cook for about 30 seconds until fragrant, then add the peas.
Fry the rice: Add the cold rice to the hot skillet. Spread it across the cooking surface and leave it undisturbed for about 30 seconds. Toss and cook for 2 to 3 minutes, breaking apart any clumps, until the rice is hot and the grains are separated.
Season the fried rice: Drizzle the soy sauce over the rice and add 2 tablespoons of reserved oxtail gravy. Toss immediately so the seasonings coat the rice without making it soggy. Return the browned oxtail and scrambled eggs to the skillet and cook for another 1 to 2 minutes, until thoroughly heated.
Finish and serve: Turn off the heat. Add the toasted sesame oil, black pepper, and green parts of the scallions. Taste and add salt only if needed. Serve hot with Caribbean hot pepper sauce, if desired.