1. Arrange the ribs in a nonreactive dish and season each side generously with salt, pepper, thyme, and rosemary. Cover and refrigerate overnight. Let the meat sit at room temperature for 1 hour before cooking. Preheat the oven to 350°F and set the rack on the bottom rung.
2. Coat a large Dutch oven or wide ovenproof pot with olive oil and set over medium-high heat. Working in batches, add the ribs to the pot and cook each side for 2 to 3 minutes, until browned all over. Remove the ribs with tongs and set aside. Add the carrots, celery, leeks, and garlic and sauté for 5 minutes, or until the leeks are browned and fragrant. Stir in the wine, scraping up the browned bits on the bottom of the pot. Add the stock, tomato paste, and bay leaf. Return the ribs to the pot and bring to a boil.
3. Cover and place the pot in the oven. Braise for 2 hours, turning the ribs halfway through. Uncover and cook for 45 minutes more to reduce the sauce. Test the doneness by dragging a fork along the meat. If it shreds easily, or the bones fall out easily, they are done. Skim off any fat and season with salt and pepper to taste.
4. To make the puree, fill a pot with cold water and add the parsnips and turnips. Bring to a boil, partially cover, and cook for 15 minutes, or until fork tender. Drain the vegetables and transfer to a food processor. Add the stock, ghee, salt, and pepper and puree until smooth. Cover and keep warm until the meat is finished cooking. If necessary, reheat in the hot oven 15 minutes prior to the ribs finishing. Serve the short ribs over the puree and top with a spoonful of pan juices and fresh parsley.