Melt butter in saucepan over medium to low heat. Stir in flour a little at a time until smooth and then remove from the heat. Add broth and milk a little at a time while stirring to keep mixture smooth. Return to heat and bring sauce to a gentle boil, stirring constantly until sauce thickens. Add pepper and salt to taste. Stir in mushrooms or chicken depending on which soup you want to make.
Note: This soup base can be used as a substitute for 1 can of cream of mushroom soup or cream of chicken in your casserole recipes or any other recipe that calls for them. Recipe can be doublede but be very careful to stir and keep it from getting thicker than you want. Add a little more milk and broth if the soup gets too thick, but only a little at a time.