In a small saucepan, melt butter over medium-high heat (do not allow it to brown).
Add flour and whisk to form a paste. Continue to cook, stirring, until raw flour scent is gone, about 1 minute.
Whisking constantly, add milk in a thin, steady stream, or in increments of a couple of tablespoons at a time, whisking thoroughly and getting into all corners of the pan to maintain a homogeneous texture.
Heat, stirring, until sauce comes to a simmer and begins to thicken slightly.
Reduce heat to low and cook, stirring, until sauce is thick enough to coat the back of a wooden spoon, about 3 minutes.
Season with salt and pepper. Add nutmeg to taste, if using.
If any lumps form, simply whisk thoroughly to remove them and smooth out sauce, or use a hand blender or countertop blender if lumps are particularly large or tough.
Use sauce right away, or press a piece of plastic wrap over surface of sauce to prevent a skin from forming and keep warm until ready to use.
Sauce can be cooled and stored in a sealed container in the refrigerator for several days. Reheat very gently on the stovetop or in a microwave to use.
