Place diced potatoes in a large pot, if using raw eggs place the eggs in the pot on top of the potatoes. Add all of the broth to the pot. If it does not cover the potatoes and eggs, add water until covered. You may need to wiggle the eggs down into the potatoes.
Boil the potatoes and eggs until potatoes are fork tender and eggs are done. 25-30 min.
While the potatoes are boiling make the sauce. In a medium mixing bowl, add the mayonnaise, mustard, relish, onion, salt, and pepper; stir well to mix.
When the potatoes and eggs are done remove the eggs from the pot
Drain the potatoes and return them to the pot.
Peel and dice the eggs.
While the potatoes are still hot, add the sauce to the potatoes, stirring well.
Then fold in the diced eggs. Sprinkle with green onions to garnish if desired.
Serve from the pot or in a serving bowl.
Refrigerate any leftovers.
Notes
I tested the recipe with sweet pickle relish but it would taste great with dill relish as well.
Chicken bouillon mixed with water (follow package instructions to make 4 cups) would work if you do not have chicken broth.
You can make this recipe up to a day ahead.
Store leftovers in the refrigerator for up to five days.
Since this contains mayonnaise I do not recommend letting it sit out for more than an hour or two.