Place potatoes in a large pot and cover with cold water; season with salt. Bring to a boil; reduce heat and simmer until tender, 15-20 minutes. Drainand return to pot to dry out.
Meanwhile, combine the vinegar, mustard and smoked paprika in a bowl and whisk to combine. Whisking constantly, slowly drizzle in 3 tablespoons of olive oil. Season with salt and pepper. Drizzle 3 tablespoons of the vinaigrette over the potatoes while they are still warm; toss to coat.
Heat the remaining tablespoon of olive oil in a skillet over medium-high. Add onion; season with salt. Cook, stirring occasionally until soft, about 5 minutes.
To assemble, combine watercress, potatoes and onions; season with salt. Drizzle with remaining vinaigrette to taste, and sprinkle with chives.
