This potato salad takes its dressing from the French; the potatoes are infused with white wine, chicken stock, and a light vinaigrette instead of gloppy mayonnaise.
Place the potatoes in a large stockpot; cover with cold water by 2 inches. Place over high heat, and bring to a boil. Add 2 tablespoons salt, and reduce to a simmer. Cook for 15 to 30 minutes, until just barely tender. Drain into a colander. Cover with a kitchen towel, and allow to steam for 10 minutes.
Cut the potatoes in halves or quarters, depending on size. Combine the white wine and chicken stock, and pour over warm potatoes. Allow to sit for 10 minutes. Add celery, scallions, and cornichons, and toss to combine.
Combine mustards, vinegar, remaining salt, and pepper in a small bowl; whisk to combine. Gradually add olive oil, whisking constantly, until emulsified. Pour dressing over potatoes; let sit until room temperature; stir in dill. Serve cold or at room temperature.