Preheat oven to 350°F (175°C).
Season the oxtail pieces generously with salt and pepper; rub the seasoning into the meat. Dredge oxtail pieces in the flour until they are coated on all sides.
Heat the oil in a large Dutch oven and brown oxtail on all sides, in batches if necessary. Remove oxtail from the pan, and set aside on a plate.
Add the onions, celery, carrots, and parsnips to the pan and sauté for 10 minutes, or until vegetables begin to take on some colour.
Add the herbs, stir in. Then add the tomato puree, and stir again to coat the vegetables well. Next, add the wine and the beef stock; stir to mix, then bring to a boil.
Return the browned oxtail pieces to the pan. Season gently with salt and pepper, cover, and place in the oven for 3 hours.
In the final half-hour of braising, boil the potatoes and celeriac in well-salted water for about 20 minutes, or until very soft. Purée them with butter, cream, and milk; add additional salt as desired. (I like to put them through the food mill before puréing them with a hand-held mixer.)
Serve the oxtail, with plenty of the sauce, on a potato and celery root purée.