Make the roux first; melt the butter over medium heat and add the flour. Stir to combine and cook the mixture for about 3 minutes.
Remove from the stove and mix well with the cold milk. Then, bring to the boil while stirring non-stop until you get the required thickness. Season to taste with salt, pepper and nutmeg.
Mixing the hot roux with cold milk helps to avoid lumps during the cooking process. If you prepare the roux in advance and it has cooled down, then mix it with hot milk.
When ready, cover the béchamel sauce with cling film to avoid it drying out.