Rinse the oxtail pieces under cold water and pat them dry with paper towels. Season with salt and pepper.
In a large pot or Dutch oven, heat the vegetable oil over medium-high heat. Add the oxtail pieces in batches, browning them on all sides. Remove and set aside.
In the same pot, add the onion, garlic, and ginger. Sauté for about 3-4 minutes until the onion is translucent.
Add the carrots, celery, and bell pepper to the pot. Cook for another 5 minutes, stirring occasionally.
Return the browned oxtail to the pot. Stir in the soy sauce, browning sauce, allspice, thyme, bay leaf, beef broth, and diced tomatoes. Bring to a boil.
Reduce the heat to low, cover, and let simmer for 2.5 to 3 hours, or until the oxtail is tender and the meat is falling off the bone. Stir occasionally and add water if necessary to keep it from drying out.
Once cooked, remove the bay leaf and adjust seasoning with salt and pepper.
Serve hot, garnished with chopped green onions.