Béchamel Sauce:

• In a saucepan over medium heat, melt the butter.
• Add the flour and cook for about 1 minute, stirring constantly to make a roux.
• Gradually whisk in the milk until smooth.
• Season with salt and black pepper.
• Cook the sauce until thickened, about 5-7 minutes. Set aside.
• Croque Madame:
• Preheat the oven to 400°F (200°C).
• Toast the bread on both sides in a pan for five minutes.
• Lay out 2 slices of Sourdough bread and spoon a portion of the béchamel sauce over them.
• Top each with ham slices.
• Over the ham sprinkle half of the Gruyère cheese on top of the ham.
• Top each with another slice of bread.
• Spread a thin layer of béchamel on top of each sandwich.
• Sprinkle the remaining Gruyère cheese on top.
• Bake in the preheated oven for about 10-12 minutes until the cheese is melted and bubbly.
• Cooking the Eggs:
• In a skillet, melt some butter over medium heat.
• Fry the eggs to your desired doneness (usually sunny side up for a Croque Madame).
• Assembly:
• Place a fried egg on top of each baked Croque Madame.
• Serve hot