Heat the vegetable oil in a wide skillet over medium-high heat.
Add the oxtail pieces and sear until slightly browned, which shouldn’t take more than 5-6 minutes.
Transfer the oxtail to the slow cooker.
Add tomato paste, onions, carrots, garlic, thyme, allspice, and paprika to the skillet. Cook for about 2 minutes until aromatic. Pour the mixture over the oxtail.
Whisk the beef broth, Worcestershire sauce, and brown sugar in a bowl. Include the bay leaves in the slow cooker and pour in the mixture.
Cover the slow cooker and cook the oxtail mixture on low heat for 8-10 hours. You’ll know the meat will be cooked when it quickly falls off the bone.
Remove the bay leaves and season the dish with salt and pepper, as desired.