Place peeled onion on foil and coat with olive oil. Wrap tightly in foil and bake at 350 degrees for one hour. Cut potatoes into cubes and boil until done, but not too soft. When onion is done, puree with oil until smooth. Stir in onion mixture, mayo, mustard, relish, and seasonings. Gently add chopped eggs. Eat warm, or chilled.