Rub the lamb with the olive oil and season with salt and pepper. Lay a couple of handfuls of hay in a roasting tin, cover with a layer of muslin (cheesecloth) or a wire rack and put the seasoned lamb on top.
Boil the potatoes in salted water until just cooked, then strain. To smoke them, you will need a large saucepan or tray with a fitted lid, and a wire rack or metal steamer basket that fits inside but is raised from the base of the saucepan. Place the saucepan over high heat and add a handful of hay. Once it begins to smoke, ignite it with a match, quickly put the wire rack on top and add the potatoes, then cover with the lid to snuff out the flames. Place outside for 20 minutes to allow the potatoes to absorb the smoke.
Meanwhile, put the mint stalks in a medium saucepan and add the vinegar,
Toss the smoked potatoes with butter, and season with salt and pepper. Serve the lamb and potatoes with the roasting juices and the mint sauce separately in a small pot.
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