5slicesbrioche breador other country style white bread
1 1/2cupsshredded Swiss cheesegruyere works best here but your favorite Swiss will work.
Melt 2 tablespoons of the butter in a small saucepan and whisk in the flour. The mixture will have the consistency of wet sand.
Cook the mixture for 2-3 minutes over medium heat until it starts to turn golden and starts to smell nutty.
Whisk in the half and half until smooth and continue to cook until thickened.
Stir in the nutmeg and salt stirring to combine.
Spread a spoonful of the béchamel on one side of four slices of bread.
Layer the Swiss cheese and ham on two slices of bread.
Top with the remaining slices of bread with the béchamel side facing the inside of the sandwich.
Butter the top half of the sandwich with 1 tablespoon of butter for each sandwich.
Melt the remaining butter in a skillet and place the sandwiches in the skillet unbuttered side down.
Grill the sandwich for 3-4 minutes of medium-low heat.
Flip the sandwich over and grill for an additional 3 minutes until golden.
Transfer the sandwiches to a baking sheet.
Top the sandwich with another spoonful or two of béchamel coating the entire surface of the bread. This will help prevent extra well done corners. (You may have extra sauce leftover, it's fantastic on everything.)
Sprinkle with the remaining cheese.
Broil the sandwiches for 2 minutes until golden and bubbling.
While the sandwiches broil, quickly fry two eggs in a clean skillet coated with cooking spray. Be careful to keep an eye on your sandwiches....or just pull them out of the oven before you fry the eggs.
Top the sandwiches with the egg and serve immediately.
Croque Madame and Croque Monsieur are both enjoyed just after cooking.