Scrub potatoes and put in a 3- to 4-quart pan. Add enough water to barely cover potatoes and bring to a boil over high heat. Cover, reduce heat, and simmer until potatoes are tender when pierced, about 40 minutes.
Meanwhile, rinse watercress, drain, and discard discolored or bruised leaves and stems. Pinch off 1 to 2 cups leaves, wrap in a towel, enclose in a plastic bag, and chill. Finely chop remaining watercress, including stems.
In a 1- to 2-quart pan, combine shallots, vinegar, mustard, sugar, and tarragon. Bring to a boil over high heat; reduce heat and simmer, stirring occasionally, about 1 minute. Remove from heat.
Drain cooked potatoes; when just cool enough to touch, in 10 to 15 minutes, pull off skins and discard. Cut potatoes into 1/2-inch chunks and put in a bowl. Stir in shallot mixture. Add 1/2 cup sour cream and chopped watercress; mix, and season to taste with salt. For a more moist salad, add additional sour cream or up to 1/4 cup broth and mix gently.
Scrape salad into a serving bowl and garnish with chilled watercress leaves.