Place the potatoes in a large saucepan with water to cover them by two inches and two tablespoons of salt. Set it over high heat to bring to a boil, and then lower the heat to simmer for 10 to 12 minutes, until tender when pierced with a fork.
Scoop out and set aside ⅓ cup of the cooking liquid. Drain the potatoes and place them in a large bowl. Drizzle the potatoes with the vinegar and the reserved cooking liquid, and let them stand for 10 minutes, tossing occasionally.
In a medium bowl, combine the celery, shallots, cornichons, chives, and dill and set aside. In a small bowl, whisk together the mayonnaise, sour cream, 1 teaspoon salt, and ½ teaspoon black pepper.
Add three-quarters of the vegetable and herb mixture to the potatoes, reserving the rest to add right before serving.
Stir in the dressing, incorporating any liquid in the bowl. Cover and refrigerate for at least two hours to allow the flavors to meld.
When ready to serve, add the reserved vegetable mixture and the eggs to the salad and sprinkle with extra dill, salt, and pepper to taste. Stir gently to combine. Serve cold or at room temperature.
