Heat the butter in a 3-quart saucepan over medium heat. Add the onions and celery and cook until they're tender.
Stir the broth, black pepper and potatoes in the saucepan and heat to a boil. Reduce the heat to low. Cover and cook for 15 minutes or until the potatoes are tender.
Place half of the broth mixture and half of the milk in a blender or food processor. Cover and blend until smooth. Repeat with the remaining broth mixture and remaining milk. Return to the saucepan and heat through.