The peppery flavor of watercress is complemented by the warming qualities of fresh ginger root. It brings a subtle Asian accent to this substantial soup, which can stand as supper when accompanied by chunks of bread.
In a 4- to 5-quart heavy-bottomed pot, warm the olive oil over medium heat. Stir in the leeks and cook, stirring, until they start to soften, about 5 minutes. Stir in the onions and cook 3 more minutes. Add the garlic and ginger root and cook until all the vegetables are soft, 6 to 7 minutes longer.
Stir the potatoes into the leek/onion mixture, then add 6 cups of the broth. Raise heat to high and bring to a boil. Lower heat to medium-low and simmer, covered, until potatoes are tender, about 8 to 10 minutes. Add the watercress to the pot and simmer until the leaves are wilted, about 5 minutes.
Let cool slightly, then purée in a food processor in batches. Return purée to the soup pot, add the milk, salt, pepper, and nutmeg, and warm over medium-low heat for a few minutes. If the soup is too thick for your taste, add more broth. Serve garnished with a dollop of sour cream or yogurt.