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 and part of the recipe. Most of all, this is a flavor that takes me back to a childhood picnic on the beach and feels American to me.
Arrange the potatoes in a single layer on a baking sheet and put it in the center of the oven. Meanwhile, in a food processor or blender, combine the parsley and basil leaves. Season with salt and pepper, to taste. Add the water and blend. With the motor running, pour 5 tablespoons of the olive oil through the top of the food processor in a slow, steady stream. This doesn't need to be a smooth puree. It should be a little rustic and chunky. Taste for seasoning and set aside.
In a bowl large enough to hold the potatoes, whisk together the red wine vinegar, shallots, mustard, capers, caper liquid, gherkins and gherkin liquid. Whisk in the remaining olive oil. Taste for seasoning. When the potatoes are tender and yielding when pierced with the tip of a knife, remove them from the oven. Allow them to cool for a few minutes and peel half of them. Some potato skin is a nice flavor in the salad.
Put the potatoes in the bowl with the dressing and lightly crush them with the tines of a fork. Season lightly with salt and pepper, to taste, and toss them in the dressing. Drizzle with the parsley/basil puree and stir to blend. Keep warm, at room temperature, until serving.