Melt the unsalted butter in a medium saucepan over a moderate heat until fully melted and just starting to bubble (about 1–2 minutes), taking care not to let it brown.
Whisk in the plain flour constantly for 1–2 minutes to form a pale, bubbly roux.
Gradually pour in the cold whole milk in a thin stream, whisking continuously until the sauce is smooth and free of lumps.
Increase the heat to medium–high and whisk constantly, bringing the sauce to a gentle simmer. Continue whisking until it thickens enough to coat the back of a spoon (about 5–7 minutes).
Remove the saucepan from the heat and stir in the salt, black pepper and a pinch of ground nutmeg, if using. Taste and adjust the seasoning as needed.