Heat oven to 190C/170C fan/gas 5. Pierce the lamb all over with a sharp knife and push garlic halves into the holes. Rub the oil all over the lamb and season well. Scatter half the thyme on top, than place the lamb on a wire rack over a roasting tray. Roast for 30 mins.
Meanwhile, in a small pan, bring the stock and butter just to the boil. Carefully lift out the lamb and wire rack. Tip the potatoes into the tray and pour over the buttery stock. Season and sprinkle on the remaining thyme. Mix everything well, shaking the tray until the potatoes are in an even layer. Place the rack and lamb back on top and cook for 1 hr.
After 1 hr, increase oven temp to 220C/200C fan/gas 8 and remove the lamb. Cover loosely and transfer to a warm place to rest for 30 mins before carving. Continue cooking the potatoes while the lamb rests until they are golden and starting to crisp. Return the lamb to the top of the potatoes, pour over any resting juices and carve over the potatoes so all the juices fall onto them.