How to Make It
Place cooked egg yolks, raw egg yolk, 1 tablespoon vinegar, mustard, and 1 teaspoon kosher salt in a food processor; pulse until combined. With processor running, slowly drizzle in oil until mixture is thick and smooth. Transfer to a medium bowl. Fold in capers, cornichons, chopped parsley, chopped chervil, chopped tarragon, and chopped egg whites. Stir in 2 teaspoons lemon juice and 1/2 teaspoon kosher salt. Cover and chill until ready to serve.
Rinse leeks. Trim leeks 2 inches above where the white turns to light green; halve lengthwise. Arrange leeks in a single layer in a large, shallow Dutch oven. Add butter, and sprinkle with remaining 1/2 teaspoon kosher salt. Add water to cover leeks by 1 inch. Bring to a simmer over medium. Cook until leeks are tender, 5 to 7 minutes. Drain and place leeks on a serving platter.
Drizzle leeks with remaining 1 tablespoon vinegar and a squeeze of lemon juice. Sprinkle with minced chives and flaky sea salt. Top with sauce gribiche; garnish with chervil or tarragon leaves.