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Heat grill to medium, around 160C. Lie the radicchio on a baking sheet and season. Whisk the oil and vinegar together, then drizzle over the radicchio. Grill for 5-8 mins, turning regularly – you want the veg to be softened and cooked through, but not too charred.
Serve on a large platter, topped with a scattering of thyme leaves and the fontina. Drizzle with a little more olive oil and balsamic vinegar, season, then serve.