Melt the butter in a medium sized saucepan over medium heat. Add the flour, stir until smooth and cook for five minutes but be careful not to let the flour brown. You want the flour to end up a light, golden color.
Meanwhile, in a separate pan, add the milk and bring it to a boil. As soon as the milk comes to a boil, remove it from the heat and pour it into the butter flour mixture and start whisking.This mixture will soon come to a boil and start bubbling. That's ok, just be sure to keep whisking so the sauce doesn't burn and the sauce stays smooth.The bubbling will stop but the sauce will continue to boil.
Keep cooking and whisking the sauce for 8 to 10 minutes until it thickens to the desired consistency. You may want to turn down the heat if it feels like it is cooking too fast.
At this point, remove the saucepan from the heat and season with the salt, pepper and nutmeg to taste. You should end up with a creamy, smooth sauce. It is now ready for your soup.
Be sure to give it a good whisk before using.
If you are making béchamel for a sauce and need to keep it warm, just pour it into a small container, cover the surface with plastic wrap and place it in a water bath to keep warm until you are ready to use.