Wash potatoes. Heat a pan of salted water to boiling. Add potatoes. Cover tightly; heat to boiling and cook about 5 minutes or until tender. Pour into colander and rinse in cold water to stop the cooking process. Drain well; combine in bowl with onion. Sprinkle with salt and pepper; mix with Italian salad dressing. Cover; refrigerate at least 2 hours.
Just before serving, add mayonnaise; toss until potatoes are well coated. Stir in celery and 2 of the eggs, chopped.
Slice the other 2 eggs and arrange around the top; sprinkle with paprika for a little color and a bit of freshly chopped parsley.