Preheat oven to 425°.
To prepare rack of lamb, trim fat from lamb; place lamb, meat side up, on a broiler pan. Insert meat thermometer into the thickest part of lamb, making sure thermometer does not touch bone.
Combine cranberries, 3/4 teaspoon rosemary, garlic, and shallot in a food processor; process until cranberries are chopped. Add breadcrumbs, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Spread mustard over lamb; pat breadcrumb mixture into mustard on lamb. Drizzle with 1 teaspoon olive oil.
To prepare potatoes, combine potatoes and remaining ingredients in a bowl. Arrange potatoes around lamb.
Bake lamb and potatoes at 425° for 40 minutes or until the thermometer registers 145° (medium-rare) to 160° (medium). Cover the lamb and let stand 10 minutes; slice the rack into 8 chops.