4 tablespoons butter, divided
1 rounded tablespoon all-purpose flour
1 cup milk
Salt and pepper
1/8 teaspoon fresh grated nutmeg
2 teaspoons Dijon mustard
2 slices white bread
2 large eggs
4 slices deli ham
4 slices deli Swiss cheese
Chopped parsley leaves, chives or thyme leaves, for garnish – choose from any or all on hand
Place a small saucepot over medium-low heat and melt two tablespoons butter in it. Whisk in a rounded tablespoon of flour and cook one 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 mustard. When sauce coats the back of a spoon, turn off heat.
Heat one tablespoon of butter in each of two medium size nonstick skillets, both over medium-low heat. When butter melts, add two large eggs to the first skillet, keeping the whites separate from each other. Add two slices of bread to the second skillet and toast lightly on first side, then turn the bread. Top the turned bread liberally with sauce, then place two 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 five minutes to melt cheese and set sauce and eggs.
Top the sandwiches with chopped herb(s) of your choice and serve. Spoon any leftover sauce over top of the eggs before garnishing.