Preheat oven to 350 degrees F. Sprinkle lamb with salt and pepper. heat 2 tablespoons oil in large ovenproof pot over high heat. Add lamb; brown on all sides, about 10 minutes total. Using tongs, transfer lamb to plate. Add 1 tablespoon oil to pot. Add onion, carrots, celery and garlic. Saute until vegetables brown and begin to soften, scraping up browned bits, about 10 minutes. Return lamb to pot, pushing gently into vegetables. Add tomatoes, broth, rosemary sprigs, thyme sprigs and peppercorns. Bring to a boil over high heat. Cover pot; transfer to oven. Roast until m eat is tender and pulls easily from bone, turning occasionally, about 2 hours.
Meanwhile, bring 8 cups water and salt to a boil in a large saucepan over high heat. Gradually whisk in polenta. Reduce heat to medium-low; simmer until thickened and tender, stirring frequently, about 22 minutes. Whisk in butter and minced thyme. Season with salt and pepper.
Remove lamb and herbs from pot; discard herbs. Place pot over medium-high h eat and boil until sauce is slightly thickened, about 5 minutes. Divide polenta among 6 large bowls; top each with 1 lamb shank. Pour sauce over; serve.