Dry the oxtails with paper towels. Season generously with salt and pepper. In a 6-quart Dutch oven, heat 1 tablespoon olive oil over medium to high heat.
Working in batches and avoiding crowding the pan, fry the oxtails on both sides in a heated pan until golden brown. Use tongs to transfer the oxtails to a platter and set aside.
Add the chopped onions, carrots, and celery to the pan. Cook for a few minutes until the onions become transparent.
Place the oxtails back in the pan. Combine the entire garlic cloves, stock, and wine. Combine bay leaf, thyme, and half a teaspoon salt. Bring to a simmer. Reduce the heat to low.
Cover and simmer for 3 hours, until the meat is fork tender.
Preheat the oven to 350° Fahrenheit (175° Celsius).
Preheat the oven for roasting the root vegetables about an hour before the meat is done.
Toss carrots, parsnips, and turnips in olive oil in a roasting pan. Season liberally with salt and pepper.
Roast the veggies for an hour, or until gently browned and cooked through.
When the oxtails are tender, remove them from the cooking liquid. Either skim the fat off the top using a spoon, use a fat separator to remove the fat, or refrigerate the cooking liquid for several hours until the fat solidifies and is simpler to remove.
If you're cooking ahead, simply place the stew in the refrigerator (let it get to room temperature first), with the oxtails still in it, and chill overnight. The next day, scrape out the fat, reheat, and remove the meat from the casserole.
Pour the cooking liquid into a dish through a mesh strainer, pressing down with a rubber spatula to remove any vegetable particles that have accumulated.
Discard the solids. Return the liquid to the pan and cook until reduced by half.
Then, put the oxtails back into the pan, followed by the roasted veggies. Heat on low for half an hour to let the flavors to blend.
Before serving, garnish with little chopped parsley.