1. Quarter the radicchio, leaving the root intact. Discard any leaves that fall off, or that seem tough.
2. Place the quarters into a bowl of ice water for 1 hour. This will remove some of the bitterness in the Radicchio.
3. Drain real well on Paper Towels of a clean dish towel.
4. Drizzle a little oil on one side, then place on a hot grill. Cook for about 5 minutes, until it's browned, then flip it over for another 5 minutes or so.
5. Serve warm whole, or shred it and use as part or all of a salad. I used spicy honey / mustard salad dressing for the main picture.