Making béchamel sauce is not rocket science, but the details matter. A good béchamel relies essentially on three ingredients: flour and butter, which make a roux, and full-cream milk to make the sauce.
THE BEST INGREDIENTS TO USE
The better the milk and butter, the better the béchamel sauce. Use butter with very little water content, such as Lurpak. I believe that a smooth sauce is best made with cold milk mixed into a hot roux, or hot milk mixed into a cold roux. For a thicker béchamel increase the butter and flour up to 45gm each.
A NOTE ON THE STAGES OF ROUX
A roux is one of the standard thickening agents for sauces in classic French cuisine. The flavour changes as you cook out the roux, getting nuttier as the roux darkens. A white or blond roux should be cooked long enough to remove the raw taste of the flour, but not to the point that it colours significantly. A brown roux is cooked just to the point of a light brown colour. It's used to thicken demi-glace and espagnole sauces; add stock to it and it becomes a velouté.
HOW TO MAKE BÉCHAMEL, STEP BY STEP
Step 1 To make the roux, melt 35gm cubed butter in a large saucepan over medium heat and stir with a wooden spoon until it's dark golden, with a nutty scent.
Step 2 Add 35gm plain flour (for a gluten-free béchamel, replace plain flour with 20gm potato starch and 15gm cornflour) and stir continuously over low heat to cook out the flour until it's a sandy colour and smells biscuity (3 minutes). This is known as a blond roux.
Step 3 Gradually add 500ml cold full-cream milk, stirring continuously with a whisk or wooden spoon, incorporating each addition well by stirring out lumps before adding the next, until a smooth sauce forms (the mixture will thicken a lot at first; stir vigorously and as you add more milk, the mixture will loosen).
Step 4 Increase heat to medium, season the béchamel to taste and stir continuously, making sure to stir into the edges of the pan and across the base to prevent the béchamel from catching, until sauce starts to boil.
Step 5 Reduce heat to low and then stir béchamel until a thick, smooth sauce forms (5 minutes). Taste béchamel and adjust seasoning, and add a pinch of paprika, nutmeg or ground ginger for a little extra flavour if you desire.
Step 6 To serve, béchamel can be used straight away or transferred to a container, covered closely with plastic wrap to prevent a skin forming, and refrigerated until required, for up to a week. Reheat, stirring gently, to serve.
To make a cheese sauce, allow the béchamel cool to 60 degrees by letting it stand in the pan for about 10 minutes, then add 60gms of grated hard cheese. I can say with experience that if you make it with Comté it will prove very difficult to resist eating it by the spoonful.