Croque Madame

Directions

1. 1
   For the bechamel sauce: Melt the butter in a small pot.
2. 2
   Add the onion and cook over low heat to sweat them.
3. 3
   Stir in the flour and cook for 1 to 2 minutes.
4. 4
   Slowly stir in the milk and bring to a simmer.
5. 5
   Cook until smooth and thickened, 10 to 15 minutes, and then season with salt, pepper and nutmeg, if using.
6. 6
   For the sandwich: Heat the oven to high broil.
7. 7
   Build each sandwich as follows: Spread 1 teaspoon of Dijon mustard on a piece of bread; top with 1 slice of Gruyere, 4 ounces ham, another slice of Gruyere and then a piece of bread.
8. 8
   Melt half the butter in a large skillet.
9. 9
   Add the sandwiches and toast to a golden brown.
10. 10
    Flip and brown on the second side.
11. 11
    Remove the sandwiches from the pan and place on a rimmed baking sheet.
12. 12
    Spoon 1/3 cup of the bechamel sauce over the top of each sandwich.
13. 13
    Broil the sandwiches to brulee the bechamel.
14. 14
    Meanwhile, melt the remaining 4 tablespoons butter in the skillet and cook the eggs over-easy.
15. 15
    Remove the sandwiches from the broiler and top with the over-easy eggs.