In a medium saucepan, melt 2 tablespoons of butter over low heat, then whisk in 2 tablespoons of flour to create a roux. Cook for about 1 minute until light golden.

Gradually pour in 1 cup of milk while continuously whisking. Cook for another 5 minutes until the sauce thickens and coats the back of a spoon. Add a pinch of nutmeg, salt, and a teaspoon of Dijon mustard.

Take two slices of bread and layer with a slice of ham followed by gruyère cheese. Spread a layer of béchamel on top, sandwich with another slice of bread, and cover with additional béchamel and cheese.

Preheat a skillet over medium heat, add 1 tablespoon of butter. Place the assembled sandwich in the skillet, cooking for 3-4 minutes until golden brown, then flip and cook the other side for another 3-4 minutes.

Transfer to a baking sheet and broil for 2-3 minutes to achieve a bubbly cheese topping, keeping a close eye to prevent burning.

Slice in half and serve hot with a side like salad or tomato soup.