Place eggs in a large saucepan. Cover them with cool water by 1 inch. Slowly bring water to a boil over medium heat; when the water has reached a boil, cover and remove from heat. Let sit 12 minutes, then place in a bowl of cold water.
Meanwhile, peel and dice potatoes into 1″ cubes, and add to salted boiling water. Cook until tender, then drain and allow to cool while peeling and slicing the eggs.
Chop celery and onion and add to potato mixture. Mix mayo and mustard in a small bowl (or substitute dill, parsley or other fresh herbs).
Gently combine all ingredients, and season to taste with salt & pepper.