Pre-heat the oven to 160ºC. (You can also braise the shanks over the stove or in a pressure cooker or slow cooker).
Season the lamb shanks generously with salt and pepper. Sprinkle with plain flour and toss well.
Heat a large, deep oven-proof pot/pan. Add oil and sear lamb shanks until well-browned on all sides. Remove from the pot and set aside.
In the same pan, add more oil and fry the chopped onion, celery and garlic until soft and fragrant. Add the herbs and tomato paste and stir before adding the red wine (if using) and stock. Allow to come to a simmer then add the lamb shanks into the pot. The shanks should almost be entirely submerged in the liquid.
Cover with a lid and place in the oven. (If cooking over the stove, use low heat and check on the shanks and turn them regularly. Add more stock or water if necessary.)
Allow to braise slowly for 2-3 hours. Check halfway through, once the lamb is slightly soft, add the potatoes, carrots and more stock or water if necessary.
Remove from the oven once the lamb and vegetables are tender.
Season with more salt and pepper if necessary and serve.
