I really love baking the potatoes for this salad. It avoids using a waterlogged potato. I also love the flavor that the herbs' stems give, so I leave some of them attached. Most of all, this is a flavor that takes me back to a childhood picnic on the beach and feels American to me.
Preheat the oven to 350 degrees F. Arrange the potatoes in a single layer in a baking dish and put it in the center of the oven. Bake for about 50 minutes.
Meanwhile, in a food processor (or blender), combine the parsley and basil leaves. Season with salt and white pepper, to taste. Add the water and blend. With the motor running, pour 1/2 cup of the olive oil through the top in a slow, steady stream. This doesnt need to be a smooth puree. It should be a little rustic and chunky. Taste for seasoning and add pinch of sugar. Pulse to combine and set aside.
In a serving bowl large enough to hold the potatoes, stir together the red wine vinegar, shallots, mustard, capers and liquid, and gherkins and liquid. Add 1/4 cup of the herb oil and toss. Taste for seasoning. Stir in half of the parsley/basil puree. When the potatoes are tender and yielding when pierced with the tip of a knife, after about 50 minutes, remove them from the oven. Allow them to cool for a few minutes. Peel half of them. Some potato skin is a nice flavor in the salad. Cut any big potatoes in quarters, the rest in half.
Put the potatoes in the bowl with the dressing. Season lightly with salt and pepper, to taste, and toss them in the dressing. Serve the remaining parsley/basil puree on the side. Keep at room temperature until serving.