Step 1: Untrimmed Lamb Rack
A lamb rack consists of an eye of meat (the loin muscle) attached to a series of rib bones that curl away from the meat as they extend outwards. When untrimmed, this eye of meat is covered in a thick layer of fat, stringy meat, and connective tissue that should be removed before cooking.
Step 2: Removing the Shoulder Blade
Sometimes, on large racks, the shoulder blade will be left intact. Remove this bone with by lifting with your non-knife hand and cutting underneath it using a butcher's knife or a paring knife. Save bone for stock or pets if desired.
Step 3: Removing Fat and Connective Tissue
Trim away the thick layer of fat covering the ribs by making a small incision where the shoulder rib was removed at the rib-tip end, and slowly peel away the layer with your non-knife hand. The action is more pulling and separating than slicing.
Step 5: Fine-Trimming of Fat
If the fat remains too thick in some areas, hold your knife parallel to the meat and carefully shave off excess until an even layer remains.
Step 6: Trimming Tendon
There is often a large tendon running right underneath the loin. Trim this tendon off, along with some additional fat. At this stage, your lamb rack is ready to cook. However, if you'd like to go the extra step for presentation and French the bones (strip the ends of excess meat), start by flipping the rack over so that the ribs are exposed.
Step 7: Scoring Membrane
Using the tip of your knife, score the membrane along the center of each bone by placing the tip of your knife against he bone starting about an inch and a half away from the cut end of the bones, and pulling your knife slowly and firmly down the bone to its end. Your bone should trace a path right down the center of each bone, not in between the bones.
Step 9: Trimming Fat and Membrane
Flip the rack over and use your knife to cut away the flap of fat and membrane. Discard excess fat, or render if desired (rendered lamb fat is great for roasting potatoes or playing practical jokes on your wife).
Step 10: Cleaning Bones
If you're really lucky, the fat and membrane will have come cleanly off the bones, leaving them bare and pearly white. Most of the time, little bits of meat and fat will remain stuck to the bone, which all but the most OCD will not mind. I consider myself amongst the most OCD, so I use the butt-end of my boning knife, next to the tang, to scrape every last scrap of connective tissue off the bones.
Step 11: Cutting Chops
To divide rack into smaller racks or individual chops, stand it on end, and starting from the exposed rib end, cut between ribs with smooth, single strokes. If you don't get through in one stroke, pick up your knife, place it back in the seam, and pull it again—do not saw back and forth. You'll end up with jagged edges.