Step 1: Prepare the Béchamel Sauce

• In a small saucepan, melt the butter over medium heat. Once melted, add the flour, stirring constantly for about 1-2 minutes until it forms a roux.
• Gradually whisk in the milk, continuing to stir until the sauce thickens (about 5 minutes). Season with salt, pepper, and nutmeg, then remove from heat.

Step 2: Assemble the Sandwiches

• Preheat your oven to 375°F (190°C).
• On a clean surface, lay out 6 slices of bread. Top each with a slice of ham and a slice of cheese. Place another slice of bread on top to create a sandwich.

Step 3: Bake the Sandwiches

• Place the assembled sandwiches on a baking sheet lined with parchment paper. Brush the tops with a little melted butter (optional).
• Bake in the preheated oven for 10 minutes, then flip the sandwiches and bake for an additional 5 minutes until golden brown.

Step 4: Add the Béchamel and Cheese

• Remove the sandwiches from the oven. Spoon the béchamel sauce over each sandwich and sprinkle with grated Gruyère cheese.
• Return to the oven and bake for an additional 5-10 minutes until the cheese is bubbly and golden.