Melt the butter on a medium heat in a large saucepan.
Once the butter has melted, turn the heat to low and add the flour. Using a ball whisk, whisk the flour into the butter on the low heat for 2-3 minutes to create a pale creamy roux, making sure to scrape out the corners so no flour gathers there.
Pour about 100-200ml of the milk into the roux and whisk until the mixture is smooth. Gradually pour the rest of the milk in, stopping every so often to make sure the flour is incorporating evenly. As you pour in more milk you can turn up the heat a little and switch to a balloon whisk which is more effective at smoothing out the lumps as the sauce increases. Often I use a combination of both whisks so I’m getting into the corners of the pan and smoothing out the lumps effectively.
Once all of the milk has been added then whisk in the salt, pepper and nutmeg. Continue mixing until the béchamel is smooth and creamy and switch off the heat.
For a final step you can use an immersion blender to really ensure a velvety result. This will also loosen the sauce a little but as the sauce rests it will thicken up once more.
Press cling film or baking parchment to the surface of the béchamel to stop a skin from forming on the top.
Whisk the sauce thoroughly before using or serving.