Preheat oven to 325°.
Season brisket with pepper and salt. In a Dutch oven, heat oil over medium-high heat. Brown roast on all sides. Remove from pan.
Add celery, onions, and large pinch of salt to the pan; cook and stir over medium heat until onions are good and browned. Add tomato past, garlic, bay leaves, and thyme; stir 1 minute longer.
Add wine to the pan, stirring to loosen browned bits from pan; add broth. Return roast to pan. Arrange potatoes, parsnips and carrots around roast; bring to a boil. Cook, covered, until meat is fork-tender, 2-2-1/2 hours.
Remove roast and vegetables from pan; keep warm. Discard bay leaves and skim fat from cooking juices. On stovetop, bring juices to a boil; cook until liquid is reduced by half, 10-12 minutes. Stir in vinegar and parsley; season with salt and pepper to taste.
Serve with vegetables and braising sauce.