Heat a large Dutch oven, with a lid, over medium-high heat. Season the meat generously with salt and pepper. Add the oil to the pot, lay the meat in the pan and sear on both sides until brown, about 10 minutes. Transfer the meat to a plate. Pour all but about 2 tablespoons of the oil from the pan.
Add the onion, carrots, celery, and garlic to the pan, and cook until vegetables are tender, about 8 minutes. Add the flour and with a wooden spoon scrape up any browned bits that cling to the bottom of the pot Add wine and tomatoes and cook until liquid has thickened, about 5 minutes more. Add broth, thyme, and bay leaves, bring to a boil. Return the roast to the pot, nestle it in the liquid, cover, place in the oven and cook until the roast is just tender, about 1 1/2 hours. Remove the lid and continue to cook, uncovered until tender about 1 hour more.
Meanwhile, put the carrots, turnips, onions, and parsnips on a baking sheet and toss with the olive oil, thyme, salt, and pepper. Roast on a shelf under the pot roast for the last hour, stirring occasionally, until tender throughout.
Transfer the roast to a plate and cover loosely with foil. Skim the fat off the surface of the liquid and discard. Bring the sauce to a boil over medium-high heat, and cook until thickened. Stir in the parsley and vinegar, salt and pepper, to taste. Keep the roast warm in the sauce until ready to slice.
Slice the pot roast across the grain and lay on a platter, surround with the vegetables. Pour some of the sauce on top and serve the remaining in a sauceboat on the side.