Cut each radicchio through the core into 4 even wedges. Heat a large skillet over medium-high heat and add the olive oil. Place the radicchio, cut-side down, in the skillet and season with salt and pepper. Sear the radicchio until the bottoms brown and wilt slightly, about 3 minutes. Turn the wedges over and sear the other sides, about 2 minutes more. Transfer the radicchio to a plate. Add the balsamic vinegar to the pan and boil until syrupy and reduced by about half, about 1 minute. Return the radicchio to the pan and toss to glaze with the balsamic syrup. Season with salt and pepper.
Divide the radicchio among 4 plates. Using a vegetable peeler, shave large pieces of cheese over the top. Serve warm.
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