Heat the oven to 325°F. Season brisket with 3/4 teaspoon salt and pepper, then heat 1 tablespoon oil in a large Dutch oven and sear beef for 5 minutes per side; transfer to a plate.
Cook onion in the same pot for 5 minutes. Stir in garlic and tomato paste for 1 minute, then add crushed tomatoes, broth and bay leaf, scraping the bottom clean.
Return beef to the pot, bring to a simmer and cover. Braise in the oven for 2 1/2 to 3 hours until a fork slides easily into the meat, turning it halfway through.
Move the covered pot to the stove and raise the oven to 425°F. Toss rutabaga, parsnips and carrots with remaining oil and salt on a rimmed sheet and roast for 25 to 30 minutes, turning once, until browned and tender.
Transfer beef to a board and discard bay leaf. Add cabbage to the broth and simmer uncovered on the stove for 15 minutes until tender.
Cut rested brisket across its grain into short bite-size pieces, discarding any remaining hard fat. Stir beef, roasted vegetables and vinegar into the broth and simmer for 5 minutes before dividing among 8 bowls.