Position a rack in the center of the oven. Preheat the oven to 325°F. Lightly butter a broilerproof 8-inch square baking dish.
Melt in a large skillet over medium heat:
Place in the pan cut side down and cook until deeply browned:
Place the endives in the baking dish (you may have to do two layers of endive) and pour in:
Cover with foil and bake until tender, about 45 minutes. While the endives cook, prepare:
When the endives are tender, pour off any liquid in the baking dish. If desired, wrap each endive half in:
Spoon the white sauce over the endives, and sprinkle with:
Turn on the broiler, return the dish to the oven, and allow the cheese to melt and brown.