Place the potatoes in a big saucepan, filling it with cold water. Add a teaspoon of salt. Bring it to a boil and cook until you can easily insert a fork, which should take around 12 to 15 minutes.
After draining them, let them cool for about ten minutes. They should still be a little warm.
In a large bowl, combine the mayonnaise, Dijon mustard, vinegar, sugar, pepper, and parsley. Stir until smooth.
Gently mix the potatoes, pickles, celery, onion, and eggs in the dressing. Be careful not to mash any of the ingredients.
For the best flavor, chill the mixture for a minimum of two hours and up to overnight. Taste for seasoning and add more salt and pepper as necessary.