Melt the butter over medium heat and add the flour.
Let the mix cook for 1 minute, mixing constantly with a whisk. This mix is called "roux" (pronounced "roo") in french.
Remove the pot from the heat and add a drizzle of milk. Whisk together. You'll notice a dough-like mix will form at first
Add all the milk one drizzle at a time, mixing in between. When the mix is thin enough, add the rest of the milk in one go. Finish by adding a bit of nutmeg.
Return the mix to medium heat and let it come to a boil. While this happens mix constantly with your whisk.
From the moment it breaks into a boil, let it cook for a minute. Remove the bechamel sauce from the heat.
Add salt and pepper to taste.