A béchamel sauce is one of the four “mother” sauces in the traditional French cooking repertoire. The others — although we're sure you know them already — are sauce velouté (a white sauce made with stock), sauce espagnole (a brown sauce made with stock), and sauce allemande (a velouté that has been thickened with egg yolks). The béchamel sauce is simply a milk-based white sauce. And the good news is, it is incredibly easy to make. Now, you can be much fancier with your preparation, and the classic French chefs would like you to be because it produces more flavor. You can add a small onion, a bay leaf, and a clove to the milk and simmer it for 15 minutes before straining it and adding it to the roux, or you can add them to the sauce once it has been mixed and simmer that very gently for 15 to 30 minutes before you strain out the onion, bay leaf and clove. You can also throw a peeled carrot, a celery stalk, and a bouquet garni into the mix, which, of course, you also strain or fish out before you use the sauce. It is also quite traditional to use a pinch of nutmeg in the sauce, although you must use a light hand, because you don't want that flavor to dominate the sauce.
Melt butter in large pan. Stir in flour - cook for about 5 minutes. Add the 1/2 and 1/2 and whisk vigorously. If necessary or preferred, strain the sauce through a fine sieve or a chinois. Salt to taste.