Though a rack of lamb looks best frenched—meaning it’s been trimmed, with much of the meat and fat between the ribs removed—some butchers get a little over-zealous, leaving just the tiniest bit of loin on the bone.
If you go to a full-service butcher (and even some supermarkets have an actual person back there who will cut and carve for you), ask him to leave some of the meat and fat near the rib-eye. This delicious part of the rib compels you to pick up the bone and gnaw to get every last luscious bit.
Another, potentially cheaper, option is to buy a whole untrimmed rack (be sure the chine bone has been removed) and trim it yourself. Check out our video “How to French a Rack of Lamb” to see this process in action.