01 - Preheat the oven to 320°F.
02 - Pat lamb shanks dry and season generously with salt and pepper.
03 - Heat olive oil in a large ovenproof pot over medium-high heat and brown the lamb shanks on all sides. Remove and set aside.
04 - In the same pot, sauté onion, carrots, and celery for 5 minutes until softened, then add garlic and cook for an additional minute.
05 - Stir in tomato paste and cook for one minute.
06 - Pour in red wine, scraping up browned bits from the pot's bottom, then simmer for 2 to 3 minutes to slightly reduce.
07 - Add stock, chopped tomatoes, rosemary, thyme, and bay leaves. Return lamb shanks to the pot, ensuring they are mostly submerged.
08 - Bring to a simmer, cover, and transfer to the oven. Cook for 2.5 to 3 hours, turning shanks once or twice, until the meat is tender.
09 - About 30 minutes before lamb finishes, bring water and salt to a boil. Whisk in polenta gradually, reduce heat to low, and cook, stirring often, for 20–25 minutes until creamy.
10 - Stir butter, Parmesan, and chopped rosemary into polenta. Adjust seasoning as needed.
11 - Remove lamb shanks from oven; discard herb stems and bay leaves. If sauce is thin, simmer uncovered until reduced to desired thickness. Serve lamb atop rosemary polenta with sauce spooned over.