Place potatoes in a large pot, cover with water and add salt until the water tastes salty (but not too salty). Bring to a boil and cook until just tender. Don't over cook because you don't want the potatoes falling apart. I don't peel my potatoes first. I boil them with the skins on and rub the peel off after they have cooled for a bit.
When the potatoes are cooled enough to handle, cut them in chunks. Chop the boiled eggs and add to the potatoes. Add the onions, celery and green pepper.
For the dressing, mix the brown sugar, sweet pickle relish, mayonnaise and mustard. Pour over the potato mixtures. Salt and pepper to taste. Refrigerate.