Heat the oil in a large saucepan over medium high heat. Add the potato and onion, stirring to coat with the oil. Season with salt and pepper to taste. Reduce heat to medium, cover and heat for 5 minutes.
Pour in the chicken stock and the milk, bring just to a boil, reduce heat to low and simmer for 10 minutes, or until potatoes are tender. Stir in the watercress and simmer, uncovered, for 4 to 5 minutes, or until watercress is just cooked.
In small batches, transfer the soup to a blender or food processor and puree until smooth. Return the soup to the pot, season to taste, and ladle into individual bowls. (Note: Place in refrigerator if not serving at this point.)
Top each serving with a dollop of whipped cream, if desired and garnish with watercress leaves.