For the Boiled Eggs:
Bring the eggs to room temperature. In a large saucepan or rondeau, lightly season water with salt and vinegar and bring to a rapid boil. Add the eggs in small batches; the water must quickly return to a boil after the eggs are added. Cook the eggs for 6½ minutes and immediately move to an ice bath. Once cooled, remove shells and hold for service.
For the Mayonnaise:
In a food processor, pulse egg yolks and distilled vinegar until combined. Add mustard and pulse. With the machine running, slowly add olive oil until emulsified to the proper consistency. Season with lemon juice, salt and pepper to taste.
For the Celery Salt:
Using a box grater, grate the celeriac. In a bowl, mix the salt and celeriac and place in a refrigerator overnight, or as long as three days. Heat an oven to 200°F. Spread the celeriac and salt mixture on a parchment-lined baking tray. Dry in the oven for 2 to 3 hours, mixing occasionally, until the entire mixture is dry and crisp, but not singed. Cool 15 to 20 minutes. In the bowl of a food processor or spice grinder, pulse the mixture to the desired consistency. Store mixture in an airtight container.
For the Dish:
Cut the base of 3 Boiled Eggs and stand vertically in the center of the plate. Dress with Mayonnaise. Season with Celery Salt and garnish each egg with chives and a leaf of tarragon.