In a large pot, boil potatoes with enough water to cover and boil potatoes just until tender, about 15 minutes.Drain when done, and place in a bowl to chill in the refrigerator.
When the potatoes are cooled down enough to handle, but still warm, peel using a pairing knife.Then cube the potatoes.
Peel and slice hard boiled eggs in half.Place the egg yolks in a mixing bowl, and set aside the egg whites.
Mash the egg yolks, as you would for deviled eggs.
Add mayonnaise, mustard, and vinegar to the mashed egg yolks and whisk until smooth and creamy.
Fold dill relish into egg yolk mixture.
Chop the egg whites and add them in with the diced potatoes.Gently toss to combine.
Season with salt and pepper to taste.
Chill at least 1 hour or preferably overnight before serving.