01 - Set 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. Brown lamb shanks on all sides, then remove and set aside.
04 - Add diced onion, carrots, and celery to the pot and cook for 5 minutes until softened. Stir in garlic and cook for 1 additional minute.
05 - Incorporate tomato paste into the vegetables and cook for 1 minute.
06 - Pour in red wine, scraping the pot to loosen browned bits, and simmer for 2 to 3 minutes to reduce slightly.
07 - Stir in stock, chopped tomatoes, rosemary, thyme, and bay leaves. Return lamb shanks to the pot, ensuring they are mostly covered with liquid.
08 - Bring mixture to a simmer, cover, and transfer pot to the oven. Cook for 2.5 to 3 hours, turning shanks once or twice, until meat is tender.
09 - About 30 minutes before lamb finishes, bring water and salt to a boil in a saucepan. Gradually whisk in polenta, reduce heat to low, and cook, stirring often, for 20-25 minutes until creamy.
10 - Stir butter, Parmesan, and chopped rosemary into the polenta. Adjust seasoning if needed.
11 - Remove lamb from oven, discard herb stems and bay leaves. If sauce is thin, simmer uncovered until thickened. Serve lamb shanks atop rosemary polenta, spooning sauce over.