Croque Madame

Directions

1. 1
   Begin by making the bechamel sauce. Get two saucepans -- heat one on medium-low heat, and the other on medium heat. To the pan on medium-low heat, add the milk and warm it through. To the other pan, add 2 tablespoons of butter, let it melt and begin to bubble, then add the flour and mix it very well to incorporate the two.
2. 2
   Continue whisking for about two minutes, being careful not to let the flour mixture brown. Slowly add in the warm milk, and continue whisking until you everything is nice and smooth. You will whisk this for about 8 to 10 minutes, until the sauce thickens. Add in the salt, nutmeg, and the Parmesan cheese. Give it a good mix, then remove it from the heat until it is ready to be used.
3. 3
   Next, heat a large skillet over medium heat. Use 2 tablespoons of butter to butter all four slices of bread, and lay them into the skillet, butter side-down. As they begin to cook, add a tablespoon of mustard to two pieces of the bread. Lay down three slices of Gruyere on top of the mustard, then top each with four slices of the black forest ham. Let them continue cooking on the skillet, lifting to peek every couple of minutes, until golden-brown.
4. 4
   Heat your broiler. Add the slices of toasted bread to a baking sheet. Place the toasted bread on top of the bread with the mustard, cheese, and ham. Generously spread bechamel sauce over the top of each sandwich. Take half a cup of the Gruyere cheese, and add that over the bechamel sauce.
5. 5
   Place under the broiler until the cheese is nice and bubbly and everything is warmed through, roughly 4 to 6 minutes.
6. 6
   During this time, add the remaining tablespoon of butter to the skillet, and let it melt over medium-high heat. Crack the eggs, leaving the yolks whole, and continue cooking in the skillet until the whites around the yolk are cooked through, sunny side-up style. Remove the sandwich from the broiler, and place on a serving plate. Top each sandwich with an egg. Dig in!