Cut the leek into thin slices and fry briefly in 1 tablespoon butter.
Peel, quarter and add the potatoes. Deglaze with 2 liters of water. Cook over low heat.
Puree the soup in a blender to create a cream. Pour back into the pot. If necessary, add hot water and bring to the boil again. Pepper and salt. Add the remaining butter, milk and watercress and serve.