Heat the milk in a small pot with the bay leaves over a gentle heat. Turn off the heat just before it reaches a simmer. Allow the bay leaves to infuse for a few minutes, then remove them.
Melt the butter in a separate small to medium pot. Add the flour and stir to form a thick paste. Cook for 1 to 2 minutes.
Add the warm milk gradually, a little at a time, whisking between additions until smooth and thick.
Stir in the Dijon mustard, nutmeg, and grated cheese. Season with salt and white pepper. Set aside to cool completely. The sauce will thicken further as it cools.
To assemble, butter the outside of each slice of bread. On the inside of one slice, spread a thin layer of Dijon mustard, then add the cooled béchamel, followed by the ham and grated cheese. Top with the second slice of bread, buttered side out.
Spray your jaffle iron with non-stick cooking spray. Place the sandwich inside and trim any corners of bread that poke out.
Cook over a small gas burner on low heat, or over low coals, for a few minutes on each side until golden brown. Check frequently to avoid burning.
Serve immediately.