Put raisins in a small bowl, cover with warm water and let stand 30 minutes to soften. Preheat oven to 325 degrees F. Toast pine nuts on a baking sheet until golden brown and fragrant, 12 to 15 minutes.

Heat olive oil over moderate heat in a skillet large enough to hold all the radicchio in one layer. Add onion and saute until soft and sweet, about 10 minutes. Add 3 tablespoons vinegar and the sugar. Drain water from raisins and add additional water, if necessary, to make 1/4 cup. Add water to skillet. Arrange radicchio in skillet cut side down. Season well with salt and pepper. Scatter the raisins over the radicchio. Cover, adjust heat to maintain a simmer and cook until radicchio is tender, about 15 minutes. Scatter the pine nuts over the radicchio, then remove from heat and let radicchio cool to room temperature in skillet.

To serve, spoon about half of the onions, raisins and pine nuts onto a serving platter. Arrange radicchio cut side up over the onions. Top with remaining onion, raisin and pine nut mixture. Taste and sprinkle with a little more vinegar if necessary. Garnish with parsley. Serve at room temperature.