Preheat the oven to 150C/300F/Gas 3.
Heat a frying pan and then add the oil followed by the butter and allow to foam.
Add the lamb and fry for 1-2 minutes on all sides, or until golden-brown all over. Season the lamb well with salt and freshly ground black pepper, then remove from the pan and place onto a plate.
In the same frying pan, add the onion, carrot, leeks and garlic and fry until golden-brown all over. Transfer the vegetables to a large casserole dish with a lid.
Place the browned lamb on top of the vegetables in the casserole, add the rosemary and pour over the stock to cover the lamb.
Cover with the lid and place into the oven to braise for 3-4 hours, or until the lamb is very tender. Remove from the oven and leave the lamb in the stock to cool completely (preferably overnight).
The next day remove the lamb from the stock and carve into thick slices. Heat the stock up over a medium heat, then place the carved lamb onto a tray and pour over some of the stock. Cover with kitchen foil and keep warm until ready to serve.
Meanwhile, place the remaining stock from the lamb into a pan and boil to reduce the liquid volume by at least half. Season, to taste, with salt and freshly ground black pepper.
Strain the sauce into a separate pan, then add the cream. Bring to the boil again and cook to reduce the sauce a little more.
Add the capers and parsley and stir well.
For the artichoke purée, place the artichokes into a pan of cold salted water together with a squeezed half lemon. Bring to the boil and cook until very tender. Drain the artichokes and remove the half lemon.
Place the artichokes into a food processor with the butter and cream and blend until very smooth. Season, to taste, with salt and freshly ground black pepper, and a little grated nutmeg.
To serve, spoon the artichoke purée onto each plate and top each with three pieces of broccoli. Carefully lift the lamb from the stock and place alongside. Spoon the sauce over the lamb and serve.