Fried Ham and Cheese Sandwich

Melt 3 tablespoons butter in a saucepan over medium-high heat. Add flour and cook, whisking constantly, until roux is smooth, about 1 to 2 minutes. Whisk in milk and bring to a boil. Reduce heat; simmer until thickened, about 7 minutes. Add 1/2 cup Gruyere and all of the Parmesan cheese; whisk until smooth. Season to taste with nutmeg, salt and pepper.

Preheat broiler to high heat. Line a baking sheet with parchment paper.

Spread Dijon mustard on 4 bread slices and place on baking sheet. Top 4 bread slices with 2 slices of ham each and remaining Gruyere cheese. Broil until cheese begins to bubble, about 2 minutes. Top with remaining bread slice; spoon a generous amount of Bechamel sauce over the top of each sandwich. Broil until bubbly and golden brown, about 3 minutes.

Melt remaining butter in a nonstick skillet; break eggs into skillet. Cook over low heat until egg whites are completely set, about 3 minutes. Spoon melted butter over egg yolks and cook until yolks begin to thicken but are not hard. Sprinkle with salt and pepper.