How to Make It
Preheat the oven to 400°. In a medium skillet, heat 1 tablespoon of the oil until shimmering. Season the lamb with salt and pepper. Add the lamb to the skillet, fat side down, and cook over moderately high heat until richly browned, about 3 minutes. Turn the lamb fat side up and cook for 2 minutes longer. Transfer the skillet to the oven and roast the rack for about 20 minutes, until an instant-read thermometer inserted in the center of the meat registers 125° for medium-rare. Transfer the lamb to a carving board and let rest for 10 minutes.
Discard the fat in the skillet. Add the remaining 2 teaspoons of oil and the garlic and cook over moderate heat until fragrant, about 30 seconds. Add the wine, prunes and olives and simmer over moderate heat until slightly reduced, about 1 minute. Add the stock and rosemary and simmer for 1 minute. Remove the skillet from the heat and swirl in the butter, 1 tablespoon at a time. Season the sauce with salt and pepper.
Carve the lamb into chops and arrange on warmed plates. Spoon the sauce over the lamb and serve.