Peel potatoes and cut into 3/4-inch chunks. In a 3- to 4-quart pan over high heat, bring potatoes and broth to a boil; cover, reduce heat, and simmer until potatoes are tender when pierced, 18 to 25 minutes.
Meanwhile, rinse and drain watercress. Pick six tender sprigs from stems and reserve. Coarsely chop remaining watercress, including stems; you should have 2 1/2 to 3 cups. Stir chopped watercress into potato-broth mixture and cook just until watercress is bright green and wilted, about 1 minute.
Pour half the potato-watercress mixture into a blender and, holding lid closed with a towel, whirl until smooth. Pour into a bowl. Repeat to purée remaining soup; pour into bowl. Stir in buttermilk.
To serve soup hot, return to pan and stir over medium heat just until steaming (do not boil). To serve cold, cover and chill until cold, 3 to 4 hours.
Ladle into bowls. Add salt and pepper to taste. Garnish with reserved watercress sprigs.