Make the bechamel: (Can be made ahead and refrigerated for up to 2 days.)

1. In a medium saucepan or skillet, melt the butter. Add flour and stir constantly with wooden spatula, cooking the flour for a few minutes, but being careful not to allow it to brown.
2. Slowly drizzle in the milk, whisking constantly. Simmer sauce for a few minutes until thickened slightly. Remove from heat. Add Dijon (to taste) and nutmeg. Let cool to room temperature before refrigerating (if making ahead), or use immediately.

Assemble the sandwiches:

1. Heat oven to 400 degrees F.
2. Line a baking sheet with parchment paper or a Silpat baking mat.
3. Arrange slices of bread on prepared baking sheet. Spread each slice with a thin layer of bechamel sauce. Top with a few slices of ham, then 2 slices of cheese. Spread another layer of bechamel on top of the cheese. Sprinkle with grated cheese.
4. 
5. Bake until cheese has melted and begun to brown and sauce is bubbling, about 5-7 minutes.
6. Serve immediately.