Place the potatoes in a large pot. Add 1 tablespoon of the salt and enough water to cover by 2 inches. Bring to a boil. Simmer until fork-tender, about 20 minutes; drain. Place the eggs in a saucepan and add enough water to cover. Bring to a boil and cook for 8 minutes. Drain and transfer to a bowl of ice water. Peel and chop the eggs. In a food processor or blender, process the mayonnaise, mustard, yogurt, shallots, garlic, lemon juice, pepper, and the remaining salt until smooth. Halve the potatoes and place in a serving bowl. Add the dressing and combine. Add the eggs, watercress, and chives and toss. Cover and refrigerate for at least 3 hours before serving.