1. Preheat oven to 475 degrees F. In the bowl of a food processor, combine shallot, garlic, mustard, 3 tablespoons olive oil, and mint; season with salt and pepper. Pulse until a medium-textured paste forms, about 30 seconds; set aside.
2. Heat a cast-iron skillet large enough to accommodate the half-rack of ribs, over medium-high heat. Add the remaining tablespoon olive oil. Season lamb with salt and pepper, and place in the skillet, fat side down. Sear meat on both sides until well browned, 4 to 5 minutes. Remove the skillet from the heat, and transfer the lamb to a clean surface.
3. Spread the reserved mint paste on the meaty side of the lamb, and place the lamb in a shallow baking pan. Transfer to the oven, and roast until the lamb is medium rare, or until the internal temperature is 130 , 18 to 22 minutes. Remove from the oven, and place lamb on a cutting board; let rest for 5 to 10 minutes before slicing. Slice between the bones, and serve.

Yield: 4 servings