Remove the base of the endives and discard any browned outer leaves. Steam the whole endives for 15 minutes and drain.
Preheat the oven on 400F. Wrap each endive with one slice of dry-cured ham and arrange the endives in a single layer in buttered oven dish.
For the béchamel: Melt the butter on medium heat then stir in the flour and mix slowly with a wooden spoon until smooth and brownish. Remove from heat. Add one cup of hot milk at a time, whisking constantly and let the béchamel thicken. Put back on heat until the mixture thickens some more. Remove from heat again, add half of the cheese, salt, pepper and a pinch of nutmeg. The cheese will melt.
Add the bechamel on top of the endives. Top with the rest of the cheese and bake for 25-30 minutes on 400F, until golden.