Preheat the oven to 150C/130C Fan/Gas 2.
Wash the oxtail pieces and pat dry with kitchen paper. Trim off as much excess fat as possible. Put the flour in a freezer bag and season well with salt and pepper. Put half the oxtail pieces into the seasoned flour, toss well to coat then set aside on a plate. Repeat with the remaining oxtail pieces.
Heat 2 tablespoons of the oil in a large frying pan. Brown the oxtail over a medium heat for about 10 minutes, turning every now and then, until dark brown all over. You may need to add extra oil if the pan looks dry at any point during the browning step. Put the browned oxtail into a flameproof casserole dish. (You may need to do this in batches.)
Return the frying pan to a low heat and add the onions, garlic, carrots and celery. Add a little extra oil if necessary. Cook gently for 10 minutes, or until softened and lightly browned, stirring occasionally.
Tip the vegetables on top of the beef and add the thyme and bay leaves. Stir in the wine, beef stock and tomato purée. Season with salt and pepper, put the casserole on the heat and bring to a gentle simmer. Cover with a lid and cook in the centre of the oven for 3 hours. Stir after 1½ hours, turning the oxtail in the sauce.
After 3 hours, the meat should be falling off the bone and the sauce should be thick. Remove the casserole dish from the oven and transfer the oxtail pieces to a plate, set aside and keep warm.
Skim any fat that has pooled on the surface of the sauce.
Divide the oxtail pieces between six warmed plates and spoon over the sauce. Sprinkle with the chopped parsley, if using, and serve with mashed potato and steamed vegetables.