If you use small Yukon Gold potatoes rather than medium ones, you don't have to peel off the skins after cooking.Plus: More Vegetable Recipes and Tips
Put the potatoes in a large pot of cold water. Bring to a boil and cook over moderate heat until tender, 20 to 25 minutes. Drain and let cool under running water. Peel the potatoes and cut them into 1/2-inch chunks.
In a large skillet, heat the olive oil until shimmering. Add the leeks and cook over moderate heat, stirring occasionally, until tender but not browned, about 5 minutes. Let the leeks cool completely.
In a large bowl, whisk the mayonnaise with the mustard and vinegar until smooth. Add the sautéed leeks, celery, tarragon and chives and season with salt and pepper. Gently fold in the potatoes until coated. Serve the potato salad chilled or at room temperature.
The potato salad can be refrigerated overnight.