Peel the potatoes, rinse under cool water.
Chop the potatoes.
Place the potatoes in a large pot.
Add the eggs.
Boil the potatoes and eggs together. (Potatoes and eggs can be cooked separately, if desired.)
Pour in enough water to cover the potatoes and eggs.
Place the pot on the burner.
Boil on high for 10 to 12 minutes.
Carefully remove the eggs.
Boil the potatoes for an additional 5 minutes.
Drain the potatoes. Let cool.
While the potatoes are cooling, chop the onions and peel and dice the eggs.
Gently mash the potatoes into slightly smaller chunks.
Fold the eggs into the potatoes.
Fold in the onions.
Fold in the relish.
Add seasonings and gently fold in.
Add mustard and mayonnaise, fold in.
Cover the potato salad and chill for at least one hour.
Before serving, garnish with paprika and parsley.