Measure out the milk into a jug and leave out of the refrigerator for at least 15 minutes before using. You do not want it directly from the refrigerator when you mix the ingredients or it will be too cold.
Gently melt the butter in a either a saucepan or double boiler over medium-low heat on the stove or in the microwave at 50% power, checking on it every 15 seconds until almost melted. There should still be soft blocks of butter in the bowl when removed from the heat or microwave. See note 4
Gradually pour in the milk while whisking the butter continuously. Whisk for about 4 minutes until smooth and creamy. Stop whisking as soon as the mixture combines and has a smooth creamy texture. Over whisking will cause the milk and butter to separate.
If you see the milk and butter separating while whisking, simply place the mixture back onto the stove. Heat on a low setting whisking gently until the butter and milk combine again to form a smooth mixture. This should take about 30 seconds.
This mixture can now be used as is in pasta sauces, mashed potatoes, soups and casseroles.