Melt butter in a small saucepan set over medium low heat, then whisk in flour. Continue to whisk for one minute to cook out the raw flour taste.
Slowly add in chicken broth and milk while continuing to whisk to incorporate the liquid. Once all of the liquid has been added, stir in the seasonings.
Bring the soup to a simmer over medium heat and continue to cook until the mixture thickens into a gravy consistency, then remove from heat.
Notes
You can use this as a base recipe to make cream of mushroom soup by substituting mushroom broth, or cream of celery soup by using vegetable broth and celery salt.