The vibrant soup can be made up to two days ahead. When ready to serve, toss the remaining raw watercress with oil and lemon juice for the topping.
In a medium saucepan, heat 1 tablespoon oil over medium. Add leeks and season with salt and pepper. Cook, stirring occasionally, until tender, 4 to 6 minutes. Add broth, potato, and 4 cups water. Bring to a boil; reduce to a simmer and cook, partially covered, until potato is tender, 10 to 12 minutes.
Add 2 bunches watercress and cook until bright green and tender, about 3 minutes. Using a slotted spoon, transfer vegetables and a little liquid to a blender; puree until smooth and pour into a bowl. Puree remaining liquid in blender and return to pot. Stir in pureed vegetables and season soup with salt.
In a small bowl, whisk together 1 tablespoon oil and lemon juice and season with salt and pepper. Add remaining watercress and toss. Serve soup topped with watercress.
Blending the watercress and potato with some liquid first helps break them down so the soup will be smooth.