Melt the butter in a pot over low heat.
Sift the flour and add it to the butter.
Mix using a whisk to make a smooth, uniform mixture, known as a roux.
Add room temperature milk to the roux, a little at a time, and mix with a whisk. Be careful not to let any lumps form.
Once you have added all of the milk, adjust the salt and pepper, add a pinch of nutmeg and bring to a boil.
Continue cooking for a couple of minutes to thicken. When done, remove the pot from the heat and strain the béchamel if lumpy.