Ingredients
3 tablespoons salted butter
1 1/2 tablespoons all-purpose flour
1 cup whole milk
2 to 3 sprigs fresh thyme
2 tablespoons Dijon mustard
1/4 teaspoon kosher salt
1/8 teaspoon ground nutmeg
8 thick slices white bread
8 tablespoons (1 stick) salted butter, softened
12 slices deli ham
2 cups grated cheese
2 tablespoons extra-virgin olive oil or more butter
4 large eggs
2 teaspoons chopped fresh chives
2 cups microgreens Freshly cracked black pepper
Preheat the oven to 375°F. .
Make the béchamel sauce. Melt the butter in a medium skillet over medium heat. Once the butter is beginning to foam, sprinkle in the flour and cook, stirring constantly, for about 30 seconds; the mixture will clump together and bubble. Slowly add the milk, whisking until mixture is smooth. Add the thyme and continue to cook, whisking, until the sauce thickens, about 4 minutes. Whisk in mustard, salt, and nutmeg to combine. Remove the skillet from the heat and discard thyme stems.
Make the sandwiches. Spread 1 tablespoon butter onto one side of each of the bread slices. Place four of the bread slices butter side down on a baking sheet. Place three folded slices of ham on each, and cover each pile of ham with 1/4 cup grated cheese. Top with the remaining slices of bread, butter side up.
Toast sandwiches on the center rack for 6 minutes, or until the bread is lightly golden and the cheese is melted. Remove the baking sheet from the oven and turn on the broiler.
Pour the béchamel sauce evenly over all of the sandwiches. Top the sandwiches with the remaining cheese, dividing it evenly. Broil until the cheese is bubbling and beginning to brown, 3 to 4 minutes.
Meanwhile, heat the olive oil in a large skillet over medium heat. Once the oil is glistening, carefully crack the eggs into the pan. Reduce the heat to medium-low and cook until the whites are completely set and yolks begin to thicken but are not yet firm, about 5 minutes. Using a spatula, carefully transfer 1 egg on top of each sandwich.
Top the sandwiches with chives, microgreens, and black pepper before serving.
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