Preheat the oven to 450°F (230°C) and position the oven rack in the center.
In a bowl, mix the breadcrumbs, minced garlic, chopped rosemary, 1 teaspoon salt, and ¼ teaspoon pepper. Stir in 2 tablespoons of olive oil to moisten the mixture. Set aside.
½ cup fresh breadcrumbs, 2 tablespoons garlic, 2 tablespoons chopped fresh rosemary, 2 tablespoons olive oil
Season the rack of lamb with 1 teaspoon salt and 1 teaspoon pepper.
1 (7 bone) rack of lamb, 2 teaspoons salt, 1 ¼ teaspoons black pepper
Heat 2 tablespoons of olive oil in a large oven-safe skillet over high heat. Sear the lamb on all sides for 1-2 minutes. Remove from the skillet and let it rest briefly.
2 tablespoons olive oil
Brush the top of the lamb with Dijon mustard and coat evenly with the breadcrumb mixture. Cover the exposed bones with foil to prevent burning.
1 tablespoon Dijon mustard
Place the lamb bone-side down on a baking tray and roast for 12-18 minutes for medium doneness (internal temperature of 130°F (50°C). If the breadcrumbs brown too quickly, cover with foil until the last 5 minutes.
Remove from the oven and let the lamb rest for 5-7 minutes, loosely covered with foil. Carve between the ribs and serve.