Hard boil the eggs. Set aside to cool.
Bring potatoes to a boil in a large pot of well-salted water. Reduce heat to medium-high and cook until potatoes are tender, about 15-20 minutes. Drain well.
Chop eggs in a large bowl. Add onion, relish, mayonnaise, and two or three dashes of ground pepper. Add potatoes and mix well. Adjust salt as needed.