Boil a large pot of salted water, add cubed waxy potatoes, cook for 8 to 10 minutes until tender but firm. Drain and cool on a baking sheet.

In a mixing bowl, whisk together olive oil, red wine vinegar, Dijon mustard, grainy mustard, minced garlic, and cornichon juice. Season with salt and pepper.

In a large bowl, combine cooled potatoes, parsley, dill, green onions, shallots, and cornichons. Drizzle dressing over, fold gently.

Chill for at least one hour before serving to enhance flavors.