Croque Madame

Instructions

1. 1

   Preheat oven to broil with rack about 8 inches from heat source. Heat a large nonstick skillet over medium-high. Spread 1 side of bread slices evenly with 1 tbsp of the butter. Place bread slices, buttered side down, in skillet; cook until toasted and golden, 2 to 4 minutes. Transfer bread to a work surface. Wipe skillet clean.

2. 2

   Melt 1 tbsp of the butter in a small saucepan over medium until foamy. Whisk in flour; cook, whisking constantly, until light golden, about 1 minute 30 seconds. Gradually whisk in milk; bring to a simmer over medium, whisking constantly. Reduce heat to low; cook, whisking often, until thickened, about 3 minutes. Remove from heat. Add 1/4 cup of the grated Gruyère and whisk until melted. Stir salt, pepper, and nutmeg into the Mornay sauce.

3. 3

   Arrange 2 of the bread slices on a work surface, toasted side down. On each slice, spread 2 tbsp Mornay sauce evenly to cover the surface. Sprinkle with 1/4 cup grated Gruyère, and top with 2 ham slices. Spread mustard evenly on untoasted sides of remaining 2 bread slices; place, mustard side down, on top of ham-topped slices. Spread remaining Mornay sauce evenly on top of sandwiches, then top with remaining 1/4 cup grated Gruyère.

4. 4

   Transfer sandwiches to a rimmed baking sheet, and broil in preheated oven until cheese has melted and top is bubbly and browning in spots, 5 to 7 minutes.

5. 5

   Meanwhile, melt remaining 1 tbsp butter in cleaned nonstick skillet over medium-high. Crack eggs into skillet; cook, undisturbed, until whites are set but yolks are runny, about 3 minutes.

6. 6

   Top each sandwich with a fried egg; garnish with chives, flaky sea salt, and additional pepper.