Preheat oven to 350°F (175°C). In a large pot, heat olive oil over medium heat. Brown the lamb shanks on all sides.
Add onion, carrots, and garlic; sauté for 5 minutes. Pour in red wine, scraping the bottom. Simmer for 2 minutes.
Add beef broth and rosemary. Season with salt and pepper. Cover and bake for 2 hours.
Boil potatoes until tender, then drain. Mash with cream and butter until smooth. Season to taste.
Serve lamb shanks over mashed potatoes, drizzled with sauce.
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