Heat the butter in a medium soup pot over medium low heat. Add the onions and cook gently and without browning, covered, for 10 minutes, stirring occasionally.
Add 4 cups (1 liter) of water or stock and bring to a boil. Cut the potatoes into 1-inch (2.5 cm) cubes.
Carefully add to the boiling water the potatoes and the watercress.
Add salt, and simmer for 20 minutes, partially covered.
Remove from heat and purée the soup using an immersion blender (or cool and use a blender). If it seems too thick, add a bit of water and stir.
When ready to serve, heat the soup gently, serve in bowls, and add butter and cream. Or have these ingredients directly on the table so guests can help themselves.