In a large saucepan, heat the olive oil. Add the leek and cook over moderate heat, stirring, until softened, 3 minutes. Add the broth and water and bring to a boil. Add the potato, cover and simmer over low heat until tender, about 15 minutes. Add the watercress and cook until bright green, about 2 minutes.
Working in batches, puree the soup in a blender. Return the soup to the saucepan. Add the whole and skim milk and season with salt and pepper; keep warm.
Meanwhile, trim the peeled cucumber to form a rectangle. Cut the cucumber crosswise into very thin slices. In a medium bowl, combine the rice vinegar with a large pinch of salt. Add the cucumber slices and toss well. Let stand until they have softened, about 5 minutes.
Ladle the soup into bowls. Garnish with cucumber slices and serve.
3 tablespoons extra-virgin olive oil
1 large leek, white and tender green parts only, thinly sliced
2 cups low-sodium chicken broth or vegetable stock
2 cups water
One 8-ounce Yukon Gold potato, peeled and sliced 1/3 inch thick
1/2 pound watercress, coarsely chopped (5 cups)
1 cup whole milk or plant-based substitute
1 cup skim milk or plant-based substitute
Salt and freshly ground pepper
1/2 European cucumber, peeled
1 tablespoon unseasoned rice vinegar