Trim fat from lamb. With the tip of a knife, cut 1-inch-wide pockets into the lamb at 3-inch intervals; insert a slice of garlic into each of the pockets. Set aside.
For marinade, combine balsamic vinegar, oil, mustard, sugar, basil, minced garlic, salt, and pepper in a small bowl. Place the leg of lamb in a large resealable plastic bag. Pour the marinade over the lamb. Seal the bag; turn to coat the lamb. Marinate in the refrigerator for at least 8 hours or up to 24 hours, turning the bag occasionally. Drain and discard the marinade.
Preheat oven to 325°F. Place the lamb on a rack in a foil-lined shallow roasting pan. Insert an oven-going meat thermometer into the thickest portion of the leg. Roast until desired doneness. Allow 2 to 2½ hours for medium-rare doneness (140°F) or 2½ to 3 hours for medium doneness (155°F). Cover and let stand for 15 minutes before carving. The temperature of the meat after standing should be 145°F for medium-rare doneness or 160°F for medium doneness. Remove strings. Thinly slice the lamb to serve. If desired, garnish with fresh mint or basil.