There are two "traditional" ways for making cream soups that have stood the test of time. For soups or sauces containing cheeses, and for lighter gravies, start with a Bechemel Sauce. To make the sauce, melt 3 to 4 tbs. butter in a medium-hot sauce pan. Add the same amount of all-purpose flour and stir to combine. This is called a roux. Let cook for about 3 minutes, but don't brown it. Slowly add milk to the mixture while stirring with a whisk. The roux will become very thick at first, but will thin as you add more milk. Keep adding milk while stirring until you get the thickness you desire. Sprinkle in a dash or two of nutmeg to finish the Bechemel sauce.
This is one of the Mother sauces, and is so called because a host of sauces and gravies are made from it. By adding shredded cheeses, salt, and soup bases, you can turn this silky-smooth sauce into meat or poultry gravies, Alfredo Sauce, Mornay Sauce, etc.
The Bechemel can also be used as a base for seafood chowders, bisques, and cream soups. My Mother used to add things like fresh peas and or chipped beef to make creamed entre's.
The second way to make a similar product is to again make the roux, but instead of thinning with milk, thin with veal or chicken stock. This is called a veloute. Again, once the basic Mother Sauce is made, it can be added to to form a host of small, or derivative sauces.
Use a chicken-based veloute for making chicken pot pies, or chicken gravy. Thin with beef soup base for beef sauces and gravies. This is great for making stews.
To turn the same thing into a brown sauce, or Espangole, cook the roux until it browns. This will impart a nutty flavor to the finished sauce or gravy. Thin with a good beef, reduction, broth, or stock.
So, for each of these Mother Sauces, start with a four and butter roux. Cook the roux to the desired color, white for Bechemel, lightly golden for a blonde sauce, or brown to make Espangole. Season with salt, pepper, soup base, stock, broth, carrots, celery, garlic, onion, cheese, etc., depending on the final dish to be made. Add other spices and seasonings as needed.
Another completely different method of thickening gravies is to use a slurry. Slurries can be made from equal amounts of cornstarch and water (the most common thickening slurry), tapioca starch and water, potato starch and water, or rice flour and water.
The starch is mixed with the water and stirred until smoth. The slurry is then slowly poured into a flavored broth or stalk, stirring constantly. The sauce will thicken quickly. The starches have less flavor than do the roux-based starches.
I hope this helps.
Seeeeeeeya; Goodweed of the North