Heat a cast-iron griddle pan until really hot. Heat the oven to 190°C/Gas 5. Cut each radicchio head into eight wedges, keeping the root end intact. Put into a shallow bowl and season all over with a few pinches of salt, the balsamic vinegar and a drizzle of olive oil. Gently rub the radicchio wedges so that all sides are lightly oiled.
In batches, lay the squash on the hot griddle and cook for a minute or two on each side until lines appear (you are not trying to cook the squash through, just mark it). Transfer the squash to a roasting tin and gently toss with salt, pepper and just enough oil to lightly coat. Roast for 20 minutes, or until cooked through.
Meanwhile, griddle the radicchio in batches – again just a minute or two on each side to give the wedges colour. As each piece is done, lay it in the oil and vinegar in the bowl so it can soak up more of the dressing. Add the griddled radicchio to the roasting pan along with the squash for the final 10 minutes of cooking.
Put even amounts of squash and radicchio on to individual plates, sprinkle over the chopped parsley and hazelnuts, then use a vegetable peeler to shave strips of goats’ cheese over the top. Put extra balsamic vinegar on the table for those who’d like more.
Add a generous handful of winter leaves to turn it into a salad, or some robust cooked grains (pearl barley or spelt) for something a bit more substantial.