Place eggs in a saucepan and cover with cold water by one inch. Bring the water to a rolling boil over high heat, then immediately remove from heat, cover, and let stand for 12 minutes to cook through.

While the eggs are cooking, prepare an ice bath in a large bowl. After 12 minutes, transfer the cooked eggs to the ice bath and let them cool completely, which usually takes about 5 minutes.

Once cooled, gently tap and roll each egg to crack the shell, then peel them under cold running water for easier removal. Chop the peeled eggs into bite-sized pieces and set aside.

In a large bowl, combine the mayonnaise, Dijon mustard, chopped celery, red onion, fresh dill, salt, and pepper, mixing until well blended.

Add the chopped hard-boiled eggs to the mayonnaise mixture and gently fold everything together until the eggs are evenly coated. Be careful not to overmix to maintain some texture.

Taste the egg salad and adjust seasonings as needed; you might want more salt, pepper, or mustard. Serve immediately, or cover and refrigerate for at least 30 minutes to allow the flavors to meld.