Melt butter in a skillet over medium-low heat. Add mushrooms and cook until tender. Season with salt and pepper to taste.
Add the garlic and for 2 minutes.
Stir in the flour and cook for an additional 2 minutes. Whisk in the milk and chicken broth until smooth.
Bring to a boil and allow to boil for 1 minute. Remove from heat, and allow to cook for a few minutes before transferring to a jar to store in the refrigerator.
Or, allow to cool slightly and use right away in your favorite dish.