Hard-Boil the Eggs: Place eggs in a pot, cover with water, and bring to a boil. Once boiling, reduce heat and let simmer for 10 minutes.
Cool and Peel: Transfer the eggs to a bowl of ice water to cool. Once cooled, peel and chop the eggs.
Prepare the Dressing: In a bowl, combine mayonnaise, Dijon mustard, salt, and pepper. Stir until smooth.
Combine Ingredients: Add the chopped eggs, celery, and onion to the bowl. Mix gently to combine everything.
Taste and Adjust: Sample the mixture and adjust the seasoning with more salt and pepper, if needed.
Serve: Garnish with chopped parsley, if desired, and serve chilled.