Preheat oven to 400°.
To prepare roast, trim fat from lamb, and cut 16 (3/4-inch-deep) slits into lamb. Combine 1/4 cup rosemary and garlic. Spoon about 1/2 teaspoon rosemary mixture into each slit; rub lamb with any remaining rosemary mixture. Sprinkle with salt and pepper. Place roast on the rack of a broiler pan or roasting pan. Insert meat thermometer into the thickest part of lamb, making sure not to touch bone.
Bake at 400° for about 1 1/2 hours or until thermometer registers 140° (medium-rare) to 155° (medium). Let stand 15 minutes before slicing. (Temperature of lamb will increase 5° upon standing.) Remove lamb from pan, reserving 2 tablespoons drippings for sauce; scrape up browned bits with a rubber spatula. Place roast on a platter; keep warm. To prepare sauce, pour reserved drippings into a small zip-top plastic bag. Seal bag; snip off 1 corner of bag. Drain liquid into a medium saucepan, stopping before the fat layer reaches the opening; discard fat.
Add broth and rosemary sprig to drippings in pan; bring to a boil. Reduce heat, and simmer 1 minute. Combine port and cornstarch in a small bowl; add to broth mixture. Bring to a boil; cook 1 minute, stirring constantly. Discard rosemary sprig. Serve sauce with lamb.