Prepare oxtails by patting dry with paper towel and season with salt and pepper.
Heat 1-tablespoon olive oil on medium high heat in Dutch Oven or heavy-bottom stock pot with lid. Place oxtails in Dutch Oven and sear on all sides until golden brown. Be careful to not overcrowd oxtails in the pot or they won't sear. Remove oxtails to plate.
Add chopped carrots, onions and celery to pot and cook until onion is translucent.
Add oxtails back to Dutch Oven, along with whole garlic, stock, grape juice/wine, bay leaf, thyme and 1/2 tsp salt. Bring to a simmer, and then reduce heat to low. Cover and cook until meat is fork tender -- this will likely take at least 3 hours, and could take up to 8 hours. When beef is tender, remove the oxtails from the Dutch Oven and skim fat from the top. If you're making this ahead, you could also place the pot in the refrigerator and let it chill overnight. The next day, scrape off the fat and reheat.
Heat oven to 350 F. Toss carrots, turnips, and parsnips in olive oil and salt and pepper, and place in a roasting pan. Roast vegetables until they're cooked through and lightly browned, approximately 1 hour. Set aside.
Next, strain the liquid from the Dutch Oven. Pour the cooking liquid through a mesh strainer. Discard the solids (vegetable and any bits of oxtail). Return liquid to pot and simmer until reduced by half.
Add roasted vegetables to Dutch Oven, and the oxtails. Prior to adding the oxtails, decide if you'd like to serve them bone in or not. If bone-in, simply add the oxtails to the Dutch Oven. If not, you can remove the meat from the bone by using a fork or it may be easier to use your hands.
Heat on low for approximately 45-minutes to one hour. Serve with chopped parsley.