I love bitter greens when they are cooked in ways that bring out their flavor. Grilling adds that "char" that brings radicchio to life. The pickled shallots are the acidic, (and crunchy), element that makes this a great side dish with any meat or fish.
Preheat the grill to medium. Put the shallots on a flat surface and slice them into 1/2-inch thick rounds. Toss the rounds in a bowl with 1 tablespoon of the white wine vinegar, orange juice, and salt and pepper, to taste. Set aside.
In a large bowl, toss the radicchio halves in 4 tablespoons of the olive oil and season with salt and pepper, to taste. Arrange them, cut sides down, in a single layer on the grill. You want them to be in an area of the grill that is good and hot without being so hot that they flame and scorch.
Meanwhile, combine the honey and the remaining vinegar in a saucepan over medium heat and cook until the mixture begins to foam. Turn the heat to low and keep warm.
After the radicchio has grilled for 5 minutes, turn them over to the other side and cook until tender, 10 to 12 minutes. They may vary in cooking times depending on their size. What you are looking for is that the halves hold their shape somewhat, but are tender when pierced with the tip of a knife. Remove from the grill to a platter, drizzle with the honey mixture and top with the pickled shallots. You can allow this dish to "rest" for a while so it can absorb the flavors of the dressing, or enjoy it immediately.