Place the potatoes in a pot and cover them with cold salted water. Bring to a boil, reduce to a simmer, and cook for 12 to 14 minutes, or until just tender. Drain and set aside to cool.
Combine the vinegar, Dijon mustard, and whole-grain mustard. Season with salt and pepper to taste. When the potatoes are cool, quarter them, and toss them in the mustard-vinegar mixture. Refrigerate until completely cold.
Add the oil, celery, and celery leaves and toss. Serve immediately.
