In a large pot, bring water to a boil, then reduce the heat to maintain a steady simmer. Add the endive, cover, and cook until very tender, about 45 minutes. Take the endives out of the water, drain well and place over paper towels. Let the endives cool down and then, squeeze out as much liquid as possible from the endive.
Preheat the oven to 200 °C (395°F).
Roll each endive with slices of ham and then arrange in a baking dish.
To make the béchamel, melt the butter in a small, heavy saucepan over medium heat add the flour and stir it quickly into the butter with a wooden spoon or a whisk, cook, whisking constantly, for about 2 minutes. Continue whisking and add the milk and bring the mixture to a boil. Continue whisking until thickened, about 5 minutes. Whisk in the nutmeg and pepper.
Pour the béchamel over the endives and sprinkle the cheese evenly over the top. Bake until bubbly and golden brown on top, about 15 minutes.
Serve and enjoy.