Preheat the oven to 350 degrees.
Season lamb with salt and pepper. Heat the olive oil in a large, heavy skillet and sear the lamb shanks over high heat on all sides until well browned, about 6 minutes. Remove the shanks and place in an oven-proof casserole. To the skillet add the diced vegetables and saute for 3 to 4 minutes.
When the vegetables have begun to cook and wilt, add garlic, sachet of herbs and tomato paste and combine. Add the wine and beef broth and bring to a boil. Pour the boiling liquid-vegetable mixture over the shanks in the casserole and braise, covered, in the oven for 1 hour and 20 minutes.
The lamb should be fork tender, with the meat just beginning to separate from the bone. Serve with the pan juices, vegetables, toasted polenta and sprinkle generously with the rosemary and thyme.