Heat the milk in a saucepan over medium heat, until just about to boil. You’ll know it’s ready if it sends up a little steam when you stir it.
While the milk is heating, melt the butter in another saucepan over medium low heat.
Add the flour to the melted butter, whisking continuously, creating a smooth mixture. Keep whisking for another minute to let the roux cook. Be careful not to let it brown.
Begin to whisk the milk into the roux slowly, a ladleful at a time. Be patient and don’t rush. The mixture will be thick and harder to whisk at first, but thins as you add the rest of the milk.
Once all the milk is fully incorporated, season to taste with the salt and pepper. If you want to add nutmeg, go ahead and grate a good dash in at this point as well.
Keep whisking slowly until the sauce thickens. This will take about 12-15 minutes, so don’t worry if your sauce seems too thin for a while. It’s ready when it begins to stick to the whisk in a nice thick coat.
Remove from heat and use, or let cool completely before storing.