In a medium bowl, stir together the ground beef, egg and parsley. Form into four 1/2-inch-thick patties. Heat a small skillet or gas grill to medium. If using a skillet, add the EVOO to the pan; if using a grill, brush it onto the grate. Add the patties and cook, turning once, for about 8 minutes for medium to medium-well. Remove from the heat and let cool.