1. Preheat oven to 350 degrees F.
2. Heat a large Dutch oven over medium-high heat. Season shanks with salt and pepper, dredge in flour, and shake off excess. Add oil to pan and brown shanks all over, about 15 minutes. Transfer to a plate.
3. Add celery, onion, and carrots to pot and season with salt and pepper, to taste. Cook, stirring occasionally, until tender and brown, about 20 minutes. Stir in garlic, thyme, and rosemary and cook until fragrant, about 3 minutes. Add wine, increase heat to high, and scrape up browned bits in pan with a wooden spoon. Reduce heat and cook until wine lightly coats vegetables. Return shanks to pot, add broth, and bring to a simmer. Transfer pot to oven and cook, uncovered and turning shanks once about halfway through, until fork-tender, about 2 1/2 hours.
4. Transfer shanks to a plate and cover with foil to keep warm. Let sauce settle on stove top, about 10 minutes; skim fat. Bring to a boil, and cook until slightly thickened, about 5 minutes. Season with salt and pepper, to taste. Return shanks to sauce; turn to coat and heat through. Spoon sauce and vegetables over meat, scatter parsley on top and serve. Serve shanks with polenta if desired.
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