Butter a baking dish large enough to hold & endives.
Cook the endives: Bring a large pot of water to boil, add a tablespoon of salt, add the endives and simmer for 20 minutes, depending on the size of the endives. They should yield to a knife point when pricked. Drain, place stem end up and let them drain well for 10 minutes, while you make the sauce. You can also use a pressure cooker like Marie-Louise. Bring up to pressure then turn heat to low for 8 minutes.
To make the Mornay sauce: In a heavy bottomed medium saucepan, melt the butter over medium heat, then whisk in the flour. Let the flour and butter bubble, stirring, without letting it color, for about 2 minutes. You want to cook out the raw taste of the flour, but do not let the roux brown. Add the milk, whisking constantly, to avoid lumps. Continue to cook the bechamel, stirring, 4 minutes on medium heat, until it thickens to the consistency of a thick milkshake. Remove from the heat and add salt and pepper to taste, as well as several pinches of ground nutmeg. Stir ⅔ of the grated cheese to make it into a sauce Mornay. Set aside.
Preheat the oven to 400 degrees.
Remove as much water from the endives as you can by rolling them in 2 layers of paper towels and lightly pressing. To dry them out further, place them in a skillet with a pat of butter and cook over medium heat to evaporate more water. When they've browned a bit, remove from the pan to cool slightly.
Lay out the ham slices and put a small amount of sauce in a line down the center of each slice. Roll each endive in a slice of ham and place in the buttered baking dish. Cover with mornay sauce, sprinkle remaining cheese on top.
Bake for 20-30 minutes to warm through and brown the top. To brown further, pass it under the broiler briefly.
