Put the eggs in a saucepan, with water to cover, and add a pinch of salt. Cover and bring to a boil over medium heat. Remove the saucepan from the heat and allow it to sit for 10 minutes. Remove the eggs from the water and shock in an ice bath until cool. Peel and chop the eggs on a cutting board and put into a medium bowl. Set aside.
Add the potatoes to a medium pan and cover with water. Bring to a boil over medium heat and cook the potatoes until fork tender, about 10 to 15 minutes Drain and cool the potatoes on a sheet tray.
In a large serving bowl mix together the onion, celery, relish, mayonnaise, lemon juice, salt, green onions and parsley. Add eggs and cooled potatoes. Toss together and add black pepper, to taste.