Combine potato, onion, egg, cheese, and parsley in medium bowl; blend thoroughly.
Shape into 8 patties. At this point, you should refrigerate them.
Spread bread crumbs onto waxed paper. Dip croquettes in crumbs, turning to coat evenly; set aside.
Heat vegetable oil in large skillet on moderate heat. Place croquettes in hot oil; cook about 4 minutes, or until brown on each side. Serve hot.