Sauté leeks and onions in butter. Add the grated potatoes and the stock. Cook until tender, about 45 minutes.
Boil watercress in salted water for about 2 minutes. Drain and put in a blender with leek and onion mixture. Add milk and half-and-half and blend until well combined.
Serve hot or cold with a dollop of cream on each cup.
Notes
*my Great Aunt's original recipe calls for 1 tablespoon of salt, I lowered it to a teaspoon as we tend to eat low sodium in our household.