Fill a large saucepan with cold water and bring to a rolling boil over high heat.

Gently lower 6 large eggs into the boiling water using a slotted spoon to prevent cracking.

Cook the eggs for exactly 11 minutes once the water returns to a boil.

Use a slotted spoon to transfer the eggs to a bowl of ice water with a pinch of salt to stop the cooking process.

Let the eggs cool in the ice bath for at least 5 minutes, then peel under cool running water.

Slice each egg in half lengthwise and pop the yolks into a small bowl, setting the whites aside on a cutting board.

Mash the yolks with a fork until smooth, then stir in mayonnaise, lemon juice, and Dijon mustard until creamy.

Chop the egg whites into small pieces and fold into the yolk mixture along with celery, red onion, dill, tarragon, salt, black pepper, and cayenne pepper.

Taste the salad and adjust seasoning with additional salt, pepper, or lemon juice as desired.

Cover and refrigerate the egg salad for at least 30 minutes to allow flavors to meld, then garnish with minced chives before serving.