Melt the butter in a sauce pan over low heat and stir in flour until a thick paste forms. Slowly add the milk to the flour stirring constantly to make a simple white sauce. Simmer while you cut endive in half, rinse, and steam in a double boiler until wilted, about 5 min.
Arrange endive, cut side up, in a shallow baking dish, and cover with white sauce. Break the cheese into small pieces and sprinkle over sauce, top with bread crumbs, then bake in a preheated oven at 400° for about ten minutes or until lightly browned.