Season the oxtails. Pat the oxtails dry with paper towels. Season them evenly with the salt, black pepper and smoked paprika.
Brown the meat. Heat the oil in a large skillet over medium-high heat. Brown the oxtails in batches for 2–3 minutes per side. Transfer the browned pieces to the slow cooker.
Cook the aromatics. Add the chopped onion to the same skillet and cook for about three minutes. Add the garlic and tomato paste and cook for another 30 seconds.
Deglaze the skillet. Pour in the beef broth. Scrape the bottom of the skillet with a wooden spoon to release the browned bits.
Fill the slow cooker. Pour the broth and onion mixture over the oxtails. Add the Worcestershire sauce, thyme and bay leaves.
Slow cook the oxtails. Cover and cook for 8–10 hours on LOW or 5–6 hours on HIGH. Avoid opening the lid repeatedly.
Check for tenderness. Start checking after eight hours on LOW or five hours on HIGH. Test several pieces, especially the thickest center-cut oxtail. The meat should be fork-tender and pull easily from the bone.
Continue if necessary. When the thickest pieces are still resistant, cover and cook for another 30 minutes before testing again.
Remove excess fat. Transfer the tender oxtails to a plate. Skim excess fat from the surface of the cooking liquid.
Thicken the gravy. Mix the cornstarch with the cold water. Stir the slurry into the sauce and cook uncovered on HIGH for 10–15 minutes, or until slightly thickened.
Finish the dish. Return the oxtails to the gravy. Taste, adjust the seasoning and serve hot.