Place a small sauce pot over medium low heat and melt 2 tablespoons butter in it. Whisk in a rounded tablespoon of flour and cook 1 minute or so. Whisk in milk and bring to a bubble then drop heat to low. Season the sauce with salt, pepper, nutmeg and Dijon. When sauce coats back of a spoon, turn off heat.
Heat 1 tablespoon of butter in each of 2 medium nonstick skillets, both over medium low heat. When butter melts add 2 large eggs to the first skillet, keeping the whites separate from each other. To the second skillet add 2 slices bread and toast lightly on first side then turn the bread. Top turned bread liberally with sauce and 2 slices of the ham and the Swiss cheese on each slice of bread. Use a spatula to transfer the eggs to the tops of the open faced sandwiches. Cover the pan with foil and turn off heat. Let pan stand 5 minutes to melt cheese and set sauce and eggs.
Top sandwiches with chopped herb or herbs of choice and serve. Spoon any leftover sauce over top of the eggs before garnishing.