In a saucepan, melt the butter over medium heat.
Add the flour and whisk continuously for about 2-3 minutes until the mixture becomes pale and frothy, but not browned.
Gradually add the milk while whisking constantly to avoid lumps.
Continue to cook and whisk until the sauce thickens, which should take about 5-7 minutes.
Season the sauce with salt, pepper, and a pinch of nutmeg (if using). Remove from heat and set aside.
Preheat your oven to 200°C (392°F).
Lay out 4 slices of bread and spread a thin layer of butter on one side of each slice.
Place a slice of ham on top of the buttered side of 4 slices of bread.
Sprinkle a generous amount of grated cheese over the ham.
Top each with another slice of bread, buttered side up.
Pour the béchamel sauce over the assembled sandwiches, making sure to cover them evenly.
Place the sandwiches on a baking sheet and bake in the preheated oven for about 15-20 minutes, or until they are golden brown and the cheese is melted and bubbly.
Once done, remove the Croque-Monsieur sandwiches from the oven and let them cool for a minute or two before serving.
You can optionally garnish with a bit more grated cheese and a sprinkle of fresh parsley before serving.Enjoy your delicious homemade Croque-Monsieur sandwiches!