Wash six to eight medium red potatoes. If some of the potatoes are substantially larger than the others, cut them in half to speed up the cooking process.
Place in a large stockpot, cover with water, add a little salt to the water if you wish, and bring the water to a boil over medium-high heat. Turn heat down to medium and simmer potatoes in gently boiling water for 25-30 minutes. Poke potatoes with a fork to check for doneness.
Drain hot water from stockpot and cover potatoes with cool water. When potatoes have cooled for a few minutes, drain the water and set potatoes aside to dry.
While potatoes are cooking, hard-boil six eggs. When cooked, drain the hot water from the pan and cover the eggs with cool water to stop the cooking process.
Remove eggs from the water and set aside to dry. When dry, peel the eggs and place them in a large bowl. Using a pastry blender, chop the eggs into small pieces.
Add the relish, chopped onion, and mayonnaise to the bowl.
Chop the cooled red potatoes without peeling and place in the bowl. Do not mix with other ingredients yet.
Drizzle the potatoes with the dill pickle juice so the flavor is absorbed. Add mustard, salt, and pepper to the bowl and mix all together.
If the mixture seems dry, more pickle juice may be added.
Sprinkle a bit of paprika, green onion or parsley sprigs on top to add color. (optional)
Refrigerate until ready to serve.