Heat the oven to 450 degrees F. Trim the lamb of excess fat, but leave a layer of fat over the meat. Cut about halfway down the bones between the chops; this allows the meat between them to become crisp.
Put the oil, garlic, paprika, and a sprinkle of salt and pepper in a food processor and puree; add the bread and pulse a few times to make rough crumbs. Rub this mixture over the meat side of the rack and sprinkle with more salt and pepper. Put it in a roasting pan and into the oven; roast for 18 to 20 minutes. Insert an instant-read meat thermometer straight in from one end into the meatiest part. If it reads 125 degrees F or more, remove the lamb immediately. If it reads less, put the lamb back for 5 minutes, no more. Remove the lamb and let sit for 5 minutes. Serve, separating the ribs by cutting down straight through them.