Grilled Cheese with Ham and Egg (French Croque-Madame)

A croque-madame (French for "madam crunch") is a variant of the croque-monsieur dish topped with a fried egg. A croque-monsieur (French for "mister crunch") is a baked or fried boiled ham and cheese sandwich, slathered with cream sauce and baked to bubbly perfection. The dish originated in French cafés and bars as a quick snack, but this recipe scales up easily and is a great brunch for a crowd. The sandwich's first recorded appearance on a Paris café menu was in 1910. It is a true French classic and basically a very fancy grilled cheese with ham and egg, yum!

Béchamel Sauce:
2 Tbsp. unsalted butter
2 Tbsp. all-purpose flour, unbleached
1¼ cups whole milk
¾ tsp. kosher salt
¼ tsp. nutmeg, freshly ground
1 Tbsp. Dijon mustard

Sandwich:
4 oz Gruyère cheese
8 (½" thick) slices country-style or sourdough bread
8 oz cooked ham, thinly sliced

Eggs:
2 Tbsp. unsalted butter
4 eggs
black pepper, freshly ground

To Serve:
Dijon mustard

Preheat oven to 425°F (220°C). Place an oven rack in the middle of the oven. Line a baking sheet with parchment paper.

Grate 4 oz of Gruyère cheese on the large holes of a box grater and set aside for later. (If you're not a fan of Gruyère, a sharp white cheddar would make a delicious substitute.)

Make the Béchamel:  The first step to making this classic cream sauce is to make a roux, which is really just fat and flour cooked together to create a thickening agent. Melt 2 Tbsp. butter in a medium saucepan over medium-low heat. Add 2 Tbsp. all-purpose flour and cook, whisking constantly, until butter and flour are well combined and foaming but still very pale in colour, about 2 minutes.

Very slowly stream in 1¼ cups whole milk, whisking constantly (this has to be done very gradually because if you incorporate the milk into the roux too quickly, it can become very lumpy), until mixture is pale and smooth.

Continue to cook, whisking constantly, until sauce is thickened (it should leave a trail when you run your whisk through it) and shiny and the foaming has slowed down, 6-8 minutes. It’s important to keep an eye on the béchamel and stir often; otherwise, you can scorch the bottom of the pot and be left with a lumpy sauce with an unpleasant flavour. Remove from heat and stir in ¾ tsp. salt, ¼ tsp. freshly ground nutmeg, and 1 Tbsp. Dijon mustard.

Sandwich:  Using a spoon, spread béchamel over 1 side of each 8 slices of bread, making sure to cover the full surface. Transfer 4 slices, sauce side up, to the prepared baking sheet. Divide the ham evenly among the 4 bread slices on the baking sheet. Then divide the cheese into 8 even piles, and top the ham with 1/8 each. Top with remaining slices of bread sauce side up. Sprinkle remaining 1/8 of cheese over each (cheese should be inside and on top).

Bake sandwiches until cheese and sauce are lightly browned and bubbling, about 12-14 minutes (start checking often after 8 minutes, and rotate sheet as needed for even browning).

Fry the Eggs:  Melt butter in a skillet over high heat. Fry eggs, sunny side up, for about 2 minutes.

Assembly:  Top sandwiches with fried egg, season with black pepper, and serve immediately.

Serve with extra Dijon mustard for dipping alongside.

Makes 4 servings.