- Heat the butter in a 3-quart saucepan over medium heat. Add the celery and onions and cook until they're tender, stirring occasionally.
- Stir the broth, water, 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. Remove the saucepan from the heat.
- Place half the broth mixture and 3/4 cup milk into a blender or food processor. Cover and blend until the mixture is smooth. Pour the mixture into a medium bowl. Repeat with the remaining broth mixture and milk.
- Return the broth mixture to the saucepan and cook until the mixture is hot and bubbling, stirring occasionally. Sprinkle with additional sliced green onions, if desired.