Preheat the oven to 350 degrees F. Arrange the potatoes in a single layer in a baking dish and put in the center of the oven. Bake until the potatoes are tender and can be pierced with the tip of a knife, about 50 minutes.
Meanwhile, combine the parsley and basil in a food processor or blender. Season with salt and white pepper, add 2 tablespoons water and blend. With the motor running, pour the olive oil through the top in a slow, steady stream. Add the sugar and taste for seasoning. Pulse to combine and set aside. (This doesn't need to be a smooth puree: It should be a little rustic and chunky.)
In a large bowl, combine the vinegar, shallots, mustard, capers and brine, and the gherkins and brine. Add half of the parsley-basil puree and toss. Taste for seasoning.
When the potatoes are done, remove them from the oven and let cool for a few minutes. Peel half of the potatoes (some skin adds a nice flavor to the salad). Cut any big potatoes into quarters and cut the rest in half. Put the potatoes in the bowl with the dressing; season lightly with salt and pepper and gently toss. Serve at room temperature with the remaining herb puree on the side.
Photograph by Anna Williams
Recipe courtesy Alex Guarnaschelli for Food Network Magazine