You've never grilled trevisano or radicchio? I don't blame you. I pity you, but I don't blame you. They're not the most common vegetables in the world, and if you don't treat 'em right, they can be bitter, pithy (the kind of pithy you don't want), and unpleasant.
The first time I tasted radicchio that blew my mind was at the home of my good friend Deborah Krasner. We'd fired up the big pizza oven she has in the center of her living room for a make-your-own-pizza party. All of the pies were great, but the one that really blew my mind was topped with radicchio and a bit of blue cheese.
The shredded leaves turn sweet and nutty as they char. It's a really magical transformation, and one that works just as well without the pizza base. I grill mine directly over the flames of a grill. Whether you use radicchio (those things that look like little oval-shaped purple cabbages at the supermarket) or trevisano (a special variety of radicchio that's similar in color, but shaped more like a head of Romaine lettuce, and far less common), the easiest way to do it is to split the heads in half, leaving all the leaves attached at the core.
You can then grill it directly over a moderate flame. At first the leaves will dry out and char a bit, and then they'll start to release moisture as they continue to cook. Once you've flipped the heads and they're totally tender, the leaves should be dark brown and charred black in spots, with plenty of succulent juices that burst out when you bite into them.
They're good enough on their own with just a bit of salt and pepper, but I can't help breaking out the blue cheese, my best olive oil, and a drizzle of saba, an Italian condiment that is perfect for grilled meats and vegetables.