Combine chicken broth and 1/2 cup of milk in a large saucepan. Bring to a low heat boil.
Mix flour and seasonings into a small bowl and whisk with the remaining 1/2 cup milk until a smooth and thick.
Pour the flour and milk mixture into the saucepan with the broth mixture over low heat and whisk continuously 5 minutes over a simmer. The mixture will thicken a bit as it cools.