Season rack of lamb well on all sides with salt and pepper.
Heat a medium skillet over high heat and, when hot, add the oil. When the oil is almost smoking, add the rack of lamb and brown well on all sides, about 6 minutes.
Transfer the lamb to a plate and set aside to cool slightly before proceeding.
Preheat oven to 450 degrees F.
Using the back of a spoon, spread the mustard evenly over all sides of the lamb. Spread the minced garlic over the lamb in the same manner.
In a small mixing bowl combine the breadcrumbs and grated cheese and toss to thoroughly combine. Using your hands or a spoon, spread the breadcrumb mixture evenly all over the lamb, pressing so that the crumbs adhere to the meat.
Place the rack of lamb on a baking sheet and bake for 12 to 15 minutes for medium-rare.
Allow lamb to sit for 5 to 10 minutes before carving into chops to serve.