Melt butter (or other fat) in a large pot over medium heat. (If you want to add some caramelized onions, toss in about ½ cup of freshly diced sweet onions and caramelize them in the butter.)
Whisk in the flour to make a thick paste, stirring constantly so that the butter doesn’t brown or burn.
Slowly add the chicken broth and whisk smooth.
Add the milk or cream and simmer (but do not bring to a boil) over medium-low heat for just a couple of minutes. If it is too thick, add more liquid. Remember, it will get thicker as it cools.
Now reduce heat and season with salt and a dash of pepper.
Remove from heat and let it cool slightly before serving.
Notes
For gluten-free options, use cornstarch or xanthan gum instead of flour.
For dairy-free options, use all chicken broth or substitute full-fat canned coconut milk (unsweetened).