Let's cook.
Preheat your oven to 400°F (200°C).
In a small saucepan, melt 1 tablespoon of butter over medium heat. Whisk in the flour and cook for 1 minute, stirring constantly, to create a roux.
Gradually whisk in the warm milk until the sauce is smooth and thickened, about 3-5 minutes. Stir in the Dijon mustard, nutmeg, salt, and pepper. Remove from heat and set aside.
Lightly toast the sourdough bread slices in a toaster or a dry pan until golden. Spread the remaining 1 tablespoon of butter evenly over one side of each toasted bread slice.
Place the buttered bread slices on a baking sheet. Top each slice with 1 slice of ham, then generously spoon the béchamel sauce over the ham, ensuring good coverage.
Sprinkle the shredded Gruyère cheese evenly over the béchamel sauce on each tartine.
Bake in the preheated oven for 8-10 minutes, or until the cheese is melted, bubbly, and golden brown. Serve immediately.
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