Preheat the oven to 180C/350F/Gas 4.
For the lamb, heat the olive oil in a pan and add the rack of lamb along with the rosemary and garlic. Season with salt and freshly ground black pepper and sear the lamb on all sides for 2-3 minutes, or until browned all over.
Transfer the lamb into the oven to roast for 8-10 minutes (for medium), or until the lamb is golden-brown all over and cooked to your liking. Remove from the pan and allow to rest for five minutes, before carving into three chops.
For the new potatoes, cook the potatoes in a pan of boiling water for 7-9 minutes, or until tender, then drain and crush with the chives and butter. Season, to taste, with salt and freshly ground black pepper. Pack into a metal chefs' ring set on a serving plate, then carefully remove the ring.
For the sauce, heat the wine in a pan and add the stock cube. Bring to the simmer and cook for 8-10 minutes, stirring until the stock cube is dissolved, and the liquid has reduced by half. Whisk in the butter until melted and the sauce is smooth and glossy.
Serve the lamb chops arranged on top of the crushed potato tower, and spoon around the sauce. Drizzle over the olive oil just before serving.