Preheat oven to 325°F /170°C and place the rack in the middle position.
Place the lamb shanks in the oven-proof dish. Sauté them in the butter or duck fat. Add salt and pepper. When they are browned, set them aside in a plate.
Cut the vegetables into large chunks and sauté them in the same oven-proof dish. Deglaze with the muscatel wine. Let it reduce by ¾, then add the lamb stock and the fresh thyme.
Place the lamb back in the oven-proof dish and cook for 1 ½ – 2 hours, depending on the shanks’ size. The lamb is cooked when the meat falls easily off the bone.
If the sauce is too runny, continue cooking after removing the shanks.
Adjust seasoning. Serve with fresh egg pasta or potatoes sautéed in duck fat, and maple-glazed carrots.