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1
Trim the radicchio heads, discarding wilted or bruised outer leaves and slicing off the very bottom if tough and discolored (dont remove the core).
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2
Slice the heads in quarters or sixths, into wedges about 3 inches wide.
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3
Cut through the core, so the leaves are held together.
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4
Arrange a rack in the center of the oven, and heat to 375 .
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5
Put the butter and 2 tablespoons of the olive oil in the skillet, and set over moderate heat.
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6
When the butter is melted and foaming, stir in the onion and garlic and cook for a minute, then lay in all the radicchio wedges in one layer.
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7
Sprinkle on the salt, cover the pan, and cook slowly, turning the wedges over and stirring the onion every couple of minutes.
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8
After 10 minutes or so, when the radicchio is softened slightly but still firmly holding its shape, stir the vinegar with 1/2 cup water and pour into the pan.
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9
Raise the heat a bit and bring the liquid to the boil, turning the wedges and stirring.
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10
Cook for a couple more minutes, until the pan juices are reduced and syrupy and the wedges are lightly caramelized.
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11
Remove the skillet from the heat, and arrange the radicchio wedges in the baking dish in one layer.
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12
Spoon the onion all around, and pour the skillet liquid over.
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13
Drizzle on the remaining 2 tablespoons olive oil, season with freshly ground black pepper, and sprinkle the grated cheese in an even layer, covering the radicchio.
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14
Tent the dish with aluminum foil, pressing it against the sides.
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15
Bake covered for about 20 minutes, remove the foil, and bake another 5 minutes or more, until the radicchio wedges are tender and moist and glazed golden on top.
