Place eggs in medium pot. Add enough water to cover the eggs, and bring to a boil over high heat. Once the water is boiling, remove the pot from the heat and cover with the lid. Let the covered eggs sit for 10 minutes. In the meantime, fill and medium bowl with plenty of ice and water. Once the 10 minutes is up, immediately transfer the cooked eggs with a slotted spoon to the ice water bath. Let the eggs cool for 5 minutes. Remove the eggs from the ice water, and peel the eggs.
Slice the peeled eggs in half. Add the yolks to a medium bowl bowl. Dice the eggs whites, and set aside.
Using a fork, smash the egg yolks until they are creamy. Add the mayonnaise, dijon mustard, dill and lemon juice to the eggs yolks. Stir to combine. Add the green onions, celery and eggs whites and stir until combined. Finally, season the mixture with salt and pepper to taste.
Store the egg salad in a covered airtight container in the refrigerator. For best flavor, allow the egg salad to sit in the refrigerator for 1 hour before serving.