Preheat oven to 325 degrees F. If desired, score ham by making diagonal cuts 1 inch apart in fat in a diamond pattern. Place on rack in a shallow roasting pan. Insert meat thermometer. Thermometer should not touch bone. Bake until thermometer registers 125 degrees F. For rump, allow 1-1/4 to 1-1/2 hours; for shank, allow 1-3/4 to 2 hours.
Meanwhile, for glaze, in a medium saucepan stir together sugar, vinegar, and mint sprigs. Bring to boiling. Reduce heat. Boil gently, uncovered, about 30 minutes or until reduced to 1 cup. Remove from heat. Remove and discard mint. Brush ham with some of the glaze.
Bake ham for 20 to 30 minutes more or until thermometer registers 135 degrees F, brushing three more times with additional glaze. Sprinkle with pepper. Let stand 15 minutes before carving. (The meats temperature will rise 5 degrees F during standing to the safe temperature of 140 degrees F.) Serve meat on a platter layered with green tops of uncooked leeks and green onions, if desired. Sprinkle with pepper, if desired. Bring any remaining glaze to boiling and serve with ham. Makes 16 to 20 servings.