Instructions

1. 1

   In a medium saucepan, melt 3 tablespoons of butter over medium heat.

2. 2

   Sprinkle in 3 tablespoons of all-purpose flour and whisk continuously for 1-2 minutes until smooth paste forms and cooks slightly.

3. 3

   Gradually whisk in warm milk, ensuring each addition is fully incorporated before adding more.

4. 4

   Bring sauce to gentle simmer, whisking constantly, until thickened to coat back of spoon (5-7 minutes).

5. 5

   Remove from heat and stir in Dijon mustard, grated nutmeg, salt, and pepper. Set aside.

6. 6

   Preheat oven to 400°F (200°C) and line baking sheet with parchment paper.

7. 7

   Lightly butter one side of each bread slice.

8. 8

   On four bread slices (butter-side down), spread thin layer of béchamel sauce.

9. 9

   Layer two slices Gruyère cheese, followed by two slices ham.

10. 10

    Add another layer of ham, then two more slices Gruyère cheese.

11. 11

    Top with remaining bread slices, butter-side up.

12. 12

    Transfer assembled sandwiches to prepared baking sheet.

13. 13

    Bake sandwiches for 10-12 minutes until cheese is melted and bread is lightly golden.

14. 14

    Warm remaining béchamel sauce if it has cooled and thickened.

15. 15

    Remove sandwiches from oven and spread generous layer of béchamel over top of each.

16. 16

    Sprinkle extra Gruyère cheese (about 1 tablespoon per sandwich) over béchamel.

17. 17

    Return to oven and broil for 2-4 minutes until top is bubbly and golden brown.

18. 18

    Heat non-stick skillet over medium-low heat with butter or oil.

19. 19

    Carefully crack eggs into pan, keeping yolks intact. Season with salt and pepper.

20. 20

    Cook until whites are set and yolks are still runny (2-3 minutes).

21. 21

    Transfer one fried egg onto top of each Croque Madame sandwich.

22. 22

    Serve immediately while hot.