Croque Madame

Prepare the béchamel sauce by melting the butter in a small saucepan. Add the flour and stir to form a paste. Turn the heat down to medium-low and cook the paste for 5 minutes, stirring constantly. This cooks the flour and stops it from tasting raw in the sauce.
Now turn the heat up to medium and gradually add the milk a little at a time, stirring to ensure there are no lumps and that the sauce is smooth before adding another splash of milk.
Continue stirring the sauce until all the milk has been added and you a lovely smooth sauce, this will take approximately 10 minutes.
Add the grated comte cheese, a grating of the fresh nutmeg and season to taste with salt and black pepper. Now turn the heat down really low and keep the sauce warm while you prepare the sandwich.

Under a medium grill toast the 4 slices on bread on one side only. Remove from the grill and spread mustard over 2 slices on the non toasted side.
Top each with a slice or two of ham and the remaining grated Comte cheese. Place these two slices back under the grill to allow the cheese to melt. Once melted, remove from the grill.
Place the remaining 2 slices of bread over the slices containing the ham and melted cheese so that the toasted side is facing up.
Spread the béchamel sauce over the two sandwiches and then place back under the grill.
While these are grilling, quickly fry up the eggs to your liking. Remove the sandwiches from the grill and top each with a fried egg. Serve immediately.