Pre-heat the oven to 400°F.
In a medium saucepan, over medium-low heat, melt the butter and add the flour; continue to cook for about 2 minutes.
Slowly whisk in the warmed milk; allow it to thicken; about 5 minutes.
Add pepper, chives, salt, nutmeg and Dijon
Spread the bechamel on all 8 slices of the bread.
Add 2 slices of ham to 4 slices of the bread and top with some of the cheese, leaving some behind for topping.
Top the bread with the ham and cheese with the remaining bread slices, bechamel side up.
Add remaining cheese on top of the sandwiches.
Place in pre-heated oven and bake for 10 to 12 minutes.
Change oven to broiler mode; broil 1 or 2 minutes or until cheese is golden.