To hard-boil the eggs, start with cold water in a cold pot. Put your eggs in the water and turn on the stove.
When the water comes to a rapid boil, turn off the heat and allow the eggs to sit in the hot water for an additional 10 minutes.
After 10 minutes, remove the eggs from the hot water and transfer to a cold water bath to stop cooking.
Peel eggs, removing egg yolks and placing in a separate bowl. Don't worry about breaking the egg whites!
In the bowl with the egg yolks, add mayonnaise, mustard, and anchovy filets.
Mash egg yolks and filets into the mayo and mustard.
Dice egg whites and add to the mayo mix along with the celery and onion.
Taste and season with pepper and any other salt if necessary.
Refrigerate for at least 1 hour.
Assemble your sandwich or salad and enjoy!