Cooks' notes:
•Gas-grill method: Grill radicchio, covered, over moderately high heat away from direct flame as above 20 to 25 minutes total.
•Grill-pan method: Grill radicchio in batches, without cheese, in a hot well-seasoned ridged grill pan, covered, over moderate heat. Transfer as grilled, cut sides up, to a baking sheet and keep warm in a 325°F oven. When all batches are grilled, sprinkle cheese over radicchio, then heat in oven until cheese melts.