Pat the oxtail pieces dry with paper towels then season with salt and pepper.  Heat 2 tablespoons oil in a Dutch oven or a large soup pot set over medium-high heat.  Working in batches, add half of the oxtails and brown on all sides, searing to a rich brown then transfer to a plate.  Add an additional 2 tablespoons of oil to the pot and repeat with the remaining oxtail pieces.

Add half of the beef broth, wine, tomato paste, garlic, herb bundle, and bay leaves to the pot and bring to a boil.  Return the browned oxtail to the pot, then reduce the heat to low. Cover and simmer for 3 hours.  

Using tongs, transfer the cooked oxtails to a plate and reserve. Remove and discard the bay leaves and the rosemary/thyme bundle. Transfer the cooking liquid into a smaller container and place in the freezer until the fat comes to the top and solidifies (about 1 hour). 

Remove the container of liquid from the freezer and scrape off the solidified fat. Reserve the liquid which, will have formed into a jell. Transfer the oxtails to a cutting board and remove the meat. Discard the bones and any grizzle.  Reserve the oxtail meat on a plate.

Heat the remaining 2 tablespoons oil in the empty Dutch oven or soup pot and heat over medium-high.  Add onions, leeks, and celery.  Sauté until onions are translucent, about 5 minutes.  Add the carrots, parsnips, potatoes, oxtail meat, remaining beef broth and the cooking liquid.  Bring the soup to a boil, then reduce the heat to low. Cover and simmer until the vegetables are tender, stirring occasionally, about 20 minutes.

Season to taste with salt and pepper. Ladle into bowls and serve.  This oxtail soup will be even tastier the next day after all those flavors mingle together overnight.