White sauce rule of thumb...
Equal parts of fat ( and remember...butter is better!) and flour.
Tehrea re no rules as to the amount of liquid....because the ratio of flour/fat to liquid determines how thick it is.
Basic white sauce...
2 T butter melted in a small sauce pan
2 T flour added to the melted butter and cooked about 30 seconds....and 1 cup of milk added slowly, whisking all the while....and brought to a boil and cooked about 3 minutes until the sauce no longer tastes of raw flour.
Salt and pepper to taste.
NOW....you can sautee about 2 tsps of finely chopped onion with the butter before you add the flour...
Or you can add some grated cheese and a bit of sherry wine....maybe a tablespoon full...
This will be a very thick sauce....
For a thinner sauce increase the amount of milk.
Do not attempt to reduce a cream sauce or it will become thin again....flour doesn't take to being reduced down.
Not sure I understand your first sentence.

As to what dairy product to use....depends on the "richness" you want...I suggest you try a white sauce with skim milk....then one with half and half....you'll see the difference!
Also...you can made a "white sauce" which can be the base for a gravy or a cream soup or the base for a pot pie by using both milk and broth. Substitute broth for half of the milk.
And...my cheat...or secret is to add some cream cheese to a white sauce if I have used half broth in making it....adds creaminess but no additional liquid.
Linda c

I make the white sauce for my scalloped potatoes the same way as Lindac, but I use evaporated milk. If making a creamed soup, I usually use half & half or a mix of broth and a bit of cream. Sometimes it just depends on what I have on hand in the fridge when the mood for soup hits.
Kat

I do as Linda does and I always use milk never cream. I even use chicken broth sometimes or broth from boiled veggies.

The trick is equal parts butter to flour and then enough liquid, to attain the consistency you want.

What you're describing is one of the classic 'mother' sauces of French cuisine, bechamel.

In its simplest form, it's a roux of roughly equal parts butter and flour, cooked until you've driven off the moisture in the flour but not until it starts to brown, then you add milk (note: in my hands it seems to work best if the milk is hot; putting the glass measure with milk in the microwave is the simplest way to accomplish this). Add the milk, whisking it into the roux, then cooking it gently until it is thickened. Add salt, pepper, and a pinch of nutmeg if desired, and that's your basic bechamel sauce.

Bechamel is an okay sauce in and of itself, but it's also a starting point for other sauces. Add parmesan cheese and you get Mornay sauce. Add crayfish and you get Nantua sauce. Add mustard, and you get mustard sauce. You get the idea.

By the way, if you make a roux and then add chicken broth or other light stock instead of the milk, what you've made is called veloute sauce.

Here is a link that might be useful: bechamel

And if you really want to be lazy and make a fast white sauce....whick together 2 T flour and a cup and a half of cream and heat slowly, stirring constantly and simmer 3 to 5 minutes until thickened and cooked.
Not as good as the classic way....but it's a good quick sauce.

has anyone tried the technique of making little balls of butter and flour rolled up and dropping it into a broth for thickening? i make alot of brothy soups and am curious..thanks bz

I use a 2:3 butter to flour ratio because that's what Julia Child taught me. I tend to go a little shy of her guideline of 1.5T flour per cup of liquid as a starting point for a sauce of medium thickness.

Beezee, I'm sensitive to a raw flour taste (real or imagined!) so I would not use that method.

thanks for the reminder about the uncooked raw flour taste..didnt think of that...bz