Place eggs in a single layer in a saucepan and cover with cold water by at least an inch. Bring water to a rolling boil, then turn off heat, cover, and let sit for exactly 10 minutes.
Transfer eggs immediately to an ice bath and let cool for 5 minutes. This quick cooling stops the cooking process and prevents the gray ring around the yolk.
Gently tap each egg against a hard surface and roll to crack the shell all over. Peel under cold water to help remove the shells cleanly.
Coarsely chop the eggs to your preferred texture and place in a mixing bowl.
In a separate bowl, whisk together the Greek yogurt, Dijon mustard, lemon juice, salt, and pepper until smooth and well-combined.
Add the finely chopped celery, dill, and any optional add-ins to the yogurt mixture and stir until evenly distributed.
Fold the yogurt dressing into the chopped eggs using a rubber spatula, being careful not to mash the eggs too much. Aim to coat all pieces evenly.
Cover and refrigerate for at least 15-30 minutes before serving to allow the flavors to meld together.