Prepare Eggs: If you haven't already, hard boil the eggs. (Method: Place eggs in a saucepan, cover with cold water ½-inch above eggs. Bring to a rolling boil. Remove from heat, cover, and let stand 10-12 minutes. Transfer to an ice bath for 5+ minutes to cool. Peel when cool.)
Separate Yolks: Cut the cooled, peeled eggs in half lengthwise. Gently remove the yolks and place them in a medium mixing bowl. Set the egg whites aside.
Mash Yolks for Creaminess: Add the mayonnaise and mustard to the egg yolks. Using a fork, mash the mixture thoroughly until smooth and creamy. Season with a pinch of salt and pepper.
Chop Whites & Add-ins: Finely chop the reserved egg whites. Add the chopped egg whites, thinly sliced green onion, finely diced celery, and chopped fresh dill to the creamy yolk mixture.
Combine Gently: Stir everything together gently until just combined. Be careful not to overmix.
Season & Serve: Taste and adjust seasoning with more salt and pepper if needed. Serve immediately on bread or over lettuce, or chill for at least 30 minutes for flavors to meld.