In a small saucepan, melt butter over medium heat.
Stir in flour and cook for 1 minute, whisking constantly, until lightly golden.
Slowly whisk in milk, stirring until the sauce thickens (about 2 minutes).
Add salt, pepper, nutmeg (if using), and Parmesan cheese. Remove from heat and set aside.
2. Assemble the Sandwich:
Spread Dijon mustard on two slices of bread.
Layer each with ham and Gruyère cheese, then top with the second slice of bread.
3. Toast the Sandwich:
Melt butter in a pan over medium heat.
Grill the sandwich for 2-3 minutes per side until golden brown and crispy.
4. Broil with Béchamel:
Preheat the oven broiler.
Spread béchamel sauce over the top of each sandwich and sprinkle extra cheese.
Broil for 2-3 minutes until bubbly and golden.
5. Fry the Eggs & Serve:
In a pan, melt butter and fry eggs until whites are set but yolks remain runny.
Place a fried egg on top of each sandwich.
Garnish with fresh parsley and black pepper. Serve hot!
Serving and Storage Tips

Croque Madame – The Ultimate French Breakfast Sandwich
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