A classic cook-out side dish. This potato salad is best if made the day before serving so the potatoes have time to absorb the flavors of the dressing and garnishes.
Wash and clean the potatoes. Cut them in half so that all pieces are approximately the same size, in about 1 ½-inch chunks. Place them in a large pot and cover with cold water. Bring the water to a rolling boil and add the kosher salt. Let boil until knife-tender, approximately 8 minutes. Drain and place back in the pot, covering with a lid, so that the potatoes stay warm until they are dressed.
While the potatoes are boiling, whisk together the mustard, vinegar, and shallots. Add the olive oil in a slow, steady stream, whisking continuously so that the vinaigrette emulsifies. Season to taste with salt and pepper. Pour the vinaigrette over the drained hot potatoes using a spatula to gently turn the potatoes so that the vinaigrette coats them all, taking care not to crush the potatoes. Let the dressed potatoes cool to room temperature. In the meantime combined the capers, cornichons, and hard-boiled eggs. Mix them into the dressed potatoes.
Reserving some of the herbs for topping the plated dish, generously sprinkle the potato salad with the chopped herbs, gently stirring so that every potato bite will have some herbs. Scoop the potatoes into a serving platter and top with the reserved herbs. Enjoy chilled or at room temperature.