2 pounds Idaho potatoes, scrubbed
1 shallot, sliced into thin rounds
Kosher salt and white pepper
1 tablespoon Dijon mustard
1 bunch flat-leaf parsley, with about 1 inch of stems still attached, roughly chopped
2 teaspoons chopped capers
1 bunch basil, with about 1 inch of stems still attached, roughly chopped
1 teaspoon caper brine
8 1/3 tablespoons extra-virgin olive oil, divided
4 cornichons, quartered lengthwise and sliced into 1/3-inch pieces
2 tablespoons red wine vinegar
1 teaspoon cornichon brine
Preheat the oven to 400ºF.
Bake the potatoes: Arrange the potatoes in a single layer on a baking sheet. Bake until the potatoes are tender and yielding when pierced in the thickest part with the tip of a knife, about 1 hour. Remove from the oven and allow to cool for a few minutes.
Make the pesto: Meanwhile, in a food processor or blender, combine the parsley and basil. Season with salt and pepper, add 2 tablespoons water, and blend.
With the machine running, pour the olive oil (3 tablespoons) through the top of the food processor in a slow, steady stream. The texture should be a little rustic and chunky. Taste for seasoning.
Make the dressing: In a bowl large enough to hold the potatoes, whisk together the vinegar, shallots, mustard, capers and brine, and gherkins and brine with 1 tablespoon water. Whisk in the olive oil (1/3 cup). Taste for seasoning.
Finish the salad: Once the potatoes are cool enough to handle, peel half of them. (Some potato skin is a nice flavor in the salad.) Put the potatoes in the large bowl with the dressing and lightly crush them with the tines of a fork.
Season lightly with salt and pepper and toss them in the dressing. Drizzle with the pesto and stir to blend. Serve warm or at room temperature.