01 -
Preheat the oven to 375°F and position a rack in the center.
02 -
In a medium skillet over medium heat, melt the butter. Whisk in the gluten-free flour and cook for 30 seconds, stirring constantly. Slowly pour in the whole milk while whisking continuously until the mixture is smooth. Cook and whisk until the sauce thickens, about 4 minutes. Remove from heat and stir in Dijon mustard, kosher salt, and ground nutmeg.
03 -
Generously spread softened butter on one side of each bread slice. Arrange four slices, buttered side down, on a baking sheet. Evenly layer gluten-free ham and shredded Gruyère cheese onto each. Place remaining bread slices on top, buttered side up.
04 -
Transfer the sandwiches to the oven and bake for 6 minutes, or until the bread is golden brown and the cheese is melted.
05 -
Spread a generous amount of béchamel sauce over each baked sandwich. Add additional cheese if desired. Place under the broiler for 3 to 4 minutes, until the cheese is bubbling and golden-brown.
06 -
Heat a small amount of butter or oil in a skillet over medium heat. Crack eggs into the skillet and cook until the egg whites are set but the yolks remain runny, about 5 minutes.
07 -
Top each sandwich with a fried egg. Garnish with chopped chives, microgreens if using, and freshly cracked black pepper. Serve immediately for best texture and flavor.