Toasted Ham and Cheese with Fried Egg

Melt 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 and let simmer until thickened, about 7 minutes. Add 1/2 cup of grated 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 prepared baking sheet. Top each of the 4 slices with 2 slices of ham and remaining Gruyere cheese. Broil until the cheese begins to bubble and melt, about 2 minutes. Top with remaining bread slice; spoon a generous amount of Bechamel sauce over the top of each sandwich. Broil until cheese is bubbly and golden brown, about 3 minutes.

Melt butter in a nonstick skillet until sizzling; carefully break eggs into skillet, leaving yolks intact. 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.