Quarter the radicchio and cut into wedges. Gently swirl in a bowl of water and drain in a colander.
Brush sides of each wedge with some of the oil mixture. Arrange on a broiler pan and place about five inches below the heat source. Cook, watching closely, until slightly charred, about 3 ½ to five minutes. Baste the wedges with more of the oil mixture, turn and cook for another two-four minutes until they become a deep brown color, crisp yet tender inside.