Cut peeled potatoes into 1 1/2  inch cubes. Salt water and bring to a boil. Add the cubed potatoes, boil for 8 minutes and then start checking with a fork to see when they are soft to the center, but not falling apart.  Drain and cool 10 minutes. Meanwhile chop the celery, pepper, and the boiled egg. Add the mustard, pickle relish, parsley, salt and pepper to the mayonnaise. Mix well. Add everything to the slightly cooled potatoes and mix well. Cover with plastic wrap and put in the refrigerator to chill it very well. Taste and check seasonings. Potatoes generally need quite a bit of sea salt and you may want to add more mayonnaise too. You can substitute a vinaigrette of 1 C extra virgin olive oil,  1/3 C apple cider vinegar, and 2 t sugar if you like. Sprinkle parsley on top and enjoy!  Double or quadruple the recipe for this crowd pleaser!