Melt butter (or other fat) in a large pot over medium-high heat.
Add the celery, and saute’ to soften and release the flavor.
Stir in the flour to make a thick paste, whisking constantly so that the butter doesn’t brown or burn.
Slowly add the chicken broth and whisk smooth.
Add milk or cream to the celery mixture and simmer over medium-low heat for just a couple of minutes, stirring occasionally. (Do not allow it to boil.) If the mixture is too thick, add more liquid. Remember, it will get thicker as it cools.
Now reduce heat and season with salt and pepper to taste.
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).