Preheat the oven to 140C/275F/Gas 1.
Heat a little olive oil in a heavy-bottomed ovenproof pan over a moderate heat. Sear the shoulder of lamb on all sides. When coloured, remove the lamb from the pan and add the chopped onion, carrot and rosemary. Cook over a gentle heat for 4-5 minutes or until golden brown.
Add the white wine and heat until reduced by half. Put the shoulder of lamb back in the pan on top of the vegetables and cover with chicken and veal stock. Bring to the boil.
Place in the oven, cover and cook for one hour. Remove from the oven and leave to cool.
When cooled, pick the meat from the bone into small pieces. Strain the stock and discard the vegetables. Bring the stock back to the boil and skim.
For the potatoes, arrange some of the potato slices on the bottom of a square baking dish to create a thin layer. Season with salt and freshly ground black pepper and add the chopped rosemary. Add a layer of the picked lamb shoulder, then build up a further two layers of potato slices and lamb. Cover the layers with enough hot stock from the cooked shoulder to cover, reserving the rest for the sauce, and place in the oven. Cook for 30 minutes or until the potatoes are tender and the liquid has been absorbed. Keep warm.
Turn the oven up to 180C/350F/Gas 4.
Season the best end of lamb with salt and freshly ground black pepper. Heat a little vegetable oil in a heavy-bottomed pan and sear the lamb, skin-side down. Turn over and sear on all sides. Place in the oven and roast for 6-8 minutes for rare, or until cooked to your liking. When cooked, leave to rest for 15 minutes.
Meanwhile, reduce 150ml/5fl oz of the lamb stock to a sauce consistency. Cook the carrots, broad beans and baby leeks in a little of the stock until tender, then drain. Fry the mushrooms in a little olive oil, then season with salt and freshly ground black pepper.
To assemble, using a chefs' ring, cut out four cylinders from the potato and lamb layers and place one on each warm plate. Carve the best end of lamb into cutlets and position to the side of the potato cylinder. Arrange the vegetables and mushrooms around the meat. Add the capers to the reduced lamb stock and pour over the dish. Serve immediately.