In a medium saucepan, cover the potatoes with water and bring to a boil. Simmer over moderate heat until tender, about 15 minutes. Drain and peel the potatoes, then cut them into 1/4-inch coins.
In a bowl, whisk the Champagne vinegar with the mustard. Gradually add the oil, whisking until smooth. Add the scallions and the shallot and season the dressing with salt and white pepper. Add the potatoes and toss to coat. Let stand at room temperature for 10 minutes before serving.