Make the Mornay Sauce

Cup of Yum
1. In a medium-sized skillet, melt 2 tablespoons of the butter over medium-low heat.
2. Whisk in the flour, stirring often, for 1 to 2 minutes.
3. Slowly whisk in the warmed milk, and cook, whisking and stirring frequently, until thickened, about 3 to 5 minutes.
4. Remove from the heat and stir the cheese and the Dijon mustard (1 tsp).
5. Season with a pinch of salt and pepper.
6. Transfer to a bowl and cover with plastic wrap, set aside and let cool.

Make the Croque Madame Sandwiches

1. Preheat the oven to 425°F.
2. Line a rimmed baking sheet with parchment paper and arrange the bread slices in a single layer. Toast in the oven, turning once, until lightly browned on both sides, about 15 to 18 minutes. Remove from oven and set aside.
3. Spread the tops of the toasted bread with Dijon mustard.
4. Add an equal amount of the sliced ham to 2 of the bread slices. Top the ham with ¼ cup of the Mornay sauce and then sprinkle on about a ¼ cup of the cheese.
5. Top with the remaining bread slices, Dijon facing down.
6. Spread the remaining sauce over the tops of the sandwiches, and sprinkle each with the remaining cheese.
7. Return the sandwiches to the baking sheet and bake until the cheese is melty and starting to brown slightly in spots.
8. While the sandwiches are in the oven, melt 2 tablespoon of butter in the skillet. Crack and add the eggs to the skillet. Season with salt and pepper and cook until the whites have just set, about 2 to 3 minutes for sunny-side-up eggs.
9. Remove the sandwiches from the oven and use a spatula to plate each one. Top with the fried eggs, and garnish with chopped chives, if desired. Serve at once.