Pat the oxtail pieces dry with kitchen paper and season lightly with salt and pepper. Dust them with plain flour to help with browning and thickening later. This small step enhances both colour and flavour.
Heat the oil or dripping in a large, heavy based casserole over medium to high heat. Add the oxtail pieces in batches, browning them evenly on all sides. Do not overcrowd the pan. Remove and set aside once browned.
In the same pot, lower the heat slightly and add the onion, carrots, and celery. Cook for about 8 minutes until softened and golden, stirring occasionally to prevent sticking. Add the crushed garlic and cook for another minute until aromatic.
Stir in the tomato purée and cook for a further 2 minutes to remove its raw edge. Pour in the red wine, scraping up the caramelised bits from the bottom of the pan. Allow it to simmer for 5 minutes until slightly reduced.
Return the browned oxtail to the pot. Add the bay leaf, thyme, beef stock, and Worcestershire sauce. Bring the mixture to a gentle boil, then reduce to a low simmer.
Cover the pot with a tight-fitting lid and transfer it to a preheated oven at 160°C. Cook for 3 to 3½ hours until the meat is falling off the bone tender. Halfway through, skim off any surface fat for a cleaner broth.
Once cooked, carefully remove the oxtail pieces and set aside. Strain the soup through a fine sieve into another pot to achieve a smooth texture, pressing the vegetables to extract their flavour.
Allow the oxtail to cool slightly, then remove the meat from the bones and discard the fat and gristle. Return the shredded meat to the strained soup.
Simmer the soup gently on the hob for 10 minutes. If desired, mix a teaspoon of flour with a little cold water and stir in to thicken slightly. Taste and adjust with salt, pepper, or a splash more Worcestershire sauce.
Ladle the soup into warm bowls and sprinkle with chopped parsley. Serve with crusty bread or buttered rolls to soak up the rich, velvety broth. The flavours deepen further when reheated the next day.