Boil eggs. I use the 1-10-10 method: Boil 1 minute in salted water then cover. Take off heat and let set for 10 minutes with cover on. Drain water and replace with cold water and ice. Let set for 10 more minutes or longer. Place in fridge or peel if you're going to use immediately.
While waiting on boiled eggs to cool, whisk together all other ingredients in a medium bowl. Taste. Add more seasoning if needed.
Peel eggs under running water and place on paper towels to absorb extra moisture.
Slice eggs long ways when completely cooled. Scoop out egg yolk into bowl with mayo mixture. With back of spoon, mash up yolks and mayo mixture. Mix until smooth. Taste for additional seasoning if needed.
Scoop yolk mixture into halved egg whites and make smooth and semi packed. Sprinkle with additional fresh dill. Add capers, chopped olives, pimentos if desired. Refrigerate uncovered until ready to serve.