1. Melt butter and oil in a large saucepan over medium heat. Add onion; reduce heat to medium-low, and sauté, stirring occasionally, 10 minutes or until onion is tender. Add potato and celery, and cook, stirring occasionally, 5 minutes.
2. Add broth and next 3 ingredients; bring to a low boil over medium-high. Reduce heat; simmer 25 to 30 minutes or until potato is tender. Remove from heat; stir in watercress and parsley. Let cool slightly.
3. Pour soup in 2 batches into bowl of a food processor or blender, and puree until very smooth. (Or puree soup directly in pot with an immersion blender.) Pour soup back in pot to warm if serving hot, or refrigerate until ready to serve. Before serving, if soup is too thick, add more milk or stock. Garnish, if desired.