Preheat oven to 425°.
Combine first 4 ingredients in a small saucepan; bring to a boil. Cook until reduced to 1/2 cup (about 15 minutes). Remove from heat; cool slightly. Add the butter, stirring well with a whisk; keep warm.
Sprinkle lamb with rosemary, salt, and freshly ground pepper. Place lamb, meat side up, on a broiler pan coated with cooking spray. Bake at 425° for 30 minutes or until a thermometer registers 145° (medium-rare) to 160° (medium). Let stand 5 minutes. Slice rack into 8 pieces. Serve with reduction.