Preheat a grill to medium heat. When the grill is ready, lightly brush the grate with oil.
Place the endive in a shallow baking dish with 1/4 cup of water. Cover with plastic wrap, and microwave for 2 minutes, or until slightly tender. Remove from dish, and pat dry.
Wrap each whole endive with prosciutto, and pierce with a toothpick to secure. Place each piece directly on grill and cook, turning occasionally, until ham is browned and endive is tender, approximately 3 minutes.
Place in a disposable foil baking dish, and sprinkle with the cheese. Return to the grill, cover, and continue cooking until cheese has melted.