How to make basic white sauce
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3 Types of white sauces every cook should know

White sauce should be in every cook's arsenal as it is a great base for SO MANY dishes. While simple, it needs to be done correctly. It is about the technique rather than the ingredients.
Once you master these three white sauces it will open a whole new world of dishes. You may get flooded with ideas the more you make them! You can dress up simple things, transform leftovers, and make cravable casseroles people will beg for!
The white sauce technique
The basic technique is to use a saucepan to melt the butter then the flour is added and cooked over medium heat for 1 minute to 90 seconds at which point the flour taste will be gone and the flour molecules are completely coated in the fat. This is also the thickening agent for the dairy. The proportion of the thickening agent to milk, half and half or cream is what changes with each of these variations.
Once the thickening agent is ready, slowly add your dairy stirring or else it will become very lumpy and hard to smooth out again. A whisk is the best tool for this method.

You may like this post on how to make moist chicken breasts every time.
Thin white sauce
This creates a sauce that just barely coats the back of a spoon. It gives a nice mouthfeel without being cloying. Gently season with things like fresh nutmeg, bay leaf or herbs.
Serve over omelets, vegetables and potatoes.

2 Tbsp butter
2 Tbsp flour
1 cup milk
1/4 tsp salt
Follow the basic technique above.
Medium white sauce
This is a bechamel, a classic French mother sauce. This is often the base for dishes like macaroni and cheese and other casseroles. It is just dense enough to cling to everything, carry flavors and bind without being cloying. It should also be delicious without additional flavoring added. The mouthfeel and slight sweetness from the butter and milk or cream makes it a positively divine sauce.
It's also used for creamed spinach, lasagne, Croque Monsieur/Madame seafood dishes and cauliflower cheese.

2 Tbsp butter
3 Tbsp flour
1 cup milk, half and half or cream
1/4 tsp salt
Follow the basic technique above.
Thick white sauce

This form of white sauce, I think of as culinary glue. It is very thick, stiff yet tasty. It's used for dishes like croquettes to bind meat, vegetables, cheese, etc so it is firm enough to shape, bread then fry. You will notice the proportion of butter and flour to dairy is quite a bit higher and has the addition of cornstarch.
This is a good sauce to turn all types of leftovers into exciting new dishes! Just think of refashioning leftover ham, potatoes, chicken, casseroles, vegetables and even eggs with this sauce to bind, coating with crumbs (save bits of old bread ends, cracker crumbs, etc) and frying up.
The sauce gets VERY thick when it cools so don't add more liquid even if you feel tempted.
2 1/2 Tbsp butter
1/4 cup corn starch plus 1 TBSP flour
1 1/4 cup milk
1/4 tsp salt
Prepare as technique above.