In a large pot of salty water, boil the potatoes for about fifteen minutes or until they go tender but are still firm to the touch. Use a fork to gauge their softness. Drain and remove from the heat into another bowl to let them cool down.
Take a saucepan and put the eggs in it. Fill it with water to a level where the eggs are completely covered. Bring to boil and then remove from the heat. Let the eggs stand in the hot water for ten minutes so that they are completely cooked. Remove them from the pan and put into a bowl of cold water. When they cool down, peel them and chop them up. Add these eggs to the potatoes.
Make the dressing now. Whisk together lemon juice, oil, sugar, seasoned salt, Worcestershire sauce, mustard powder and black pepper in a small bowl. Add mayonnaise to this. Pour this dressing over the potato and egg mixture and then toss well to coat.
Add the green onion, celery and parsley in the end. Refrigerate for at least an hour before serving.