Season the lamb shanks with salt and freshly ground black pepper. Heat a large ovenproof casserole until smoking, add the oil and lamb shanks and cook for 2-3 minutes on each side, or until golden-brown all over.
Remove the lamb from the pan and set aside. Add the onions, carrots, swede and garlic to the pan and cook for 2-3 minutes, or until golden-brown.
Add the rosemary, bay leaves, thyme and tomato purée to the pan and cook for a further minute, then stir in the pearl barley. Cover with the chicken stock and bring to a simmer.
Cover the pan with a tight-fitting lid, then transfer to the oven to cook for at least three hours, or preferably 5-6 hours, until the lamb is very tender. (You may need to add a bit more liquid.)
Remove the pan from the oven and stir in the mint jelly and parsley. Season, to taste, with salt and freshly ground black pepper and serve.