In a medium saucepan, add two eggs and cover with salted water. Bring to a boil over medium-high heat. As soon as the water starts to boil, turn off the heat and set a timer for 7 minutes. Meanwhile, prepare a bowl with ice water. When the timer goes off, use a slotted spoon to transfer the eggs to the bowl of ice water. Allow eggs to cool for 3 minutes and then peel.
While the eggs are cooking, pick the leaves from 4 stems of parsley, and chop until you have 1 Tablespoon. Chop 1 Tablespoon capers and 1 Tablespoon cornichons (about 3). Set aside.
Separate the egg yolks from the whites. Finely chop the egg whites and set aside. Press the yolks through a fine mesh sieve into a mixing bowl. Add 1 teaspoon Dijon mustard and 2 teaspoons Champagne vinegar, and whisk to combine. Slowly drizzle in 1/4 cup extra virgin olive oil while whisking. The sauce will become thick and lighter in color as the oil emulsifies into the egg mixture.
Fold in the chopped parsley, capers, cornichons and egg whites. Season with salt and pepper.