Croque Madame

Step 1

Melt 2 tablespoons of butter in a small saucepan over medium heat until it foams and coats the bottom, about 1 minute.

Step 2

Add the flour and stir with a wooden spoon for 30 seconds until the mixture looks like wet sand and smells toasted—this is the roux.

Step 3

Pour in the milk slowly while stirring continuously to avoid lumps; keep stirring until the sauce is smooth and thick enough to coat the back of a spoon, about 3 minutes.

Step 4

Remove from heat and stir in the grated gruyere cheese until melted and uniform; season with a pinch of salt and pepper.

Step 5

Place 2 slices of bread on a cutting board; layer 2 slices of ham on each, then top each with the second slice of bread to form two closed sandwiches.

Step 6

Heat the remaining 2 tablespoons of butter in a 12-inch skillet over medium heat until it foams and slides quickly when you tilt the pan, about 1 minute.

Step 7

Carefully place both sandwiches in the skillet and cook until the bottom is golden brown and crispy, about 2 minutes—listen for a steady sizzle.

Step 8

Flip each sandwich using a wide spatula and cook the other side until golden brown and crispy, about 2 minutes.

Step 9

Spread half the warm béchamel sauce on top of each sandwich, using the back of a spoon to form an even, smooth layer covering the entire surface.

Step 10

Crack both eggs into a small bowl, beating them gently with a fork until the yolks and whites are uniform, about 30 seconds.

Step 11

Pour the beaten eggs into the skillet alongside the sandwiches (do not pour on top of them) and cook over medium heat until the whites are set and opaque but the yolk still jiggles slightly, about 3 minutes.

Step 12

Using a wide spatula, slide one fried egg on top of each sandwich, centering it on the béchamel; season the egg with a pinch of salt and pepper.

Step 13

Transfer each sandwich to a warm plate and serve immediately while the béchamel and egg are still hot.