To a large saucepan or pot, add cubed potatoes and cover with water. Season with salt, and bring to a simmer over medium heat. Simmer for about 15 minutes or until cooked through but not falling apart. Drain and allow to cool as you prep the rest of the ingredients.
Cook the eggs using your preferred method (I like to use my instant pot, or steam the eggs). Be careful not to overcook them as the yolks will be used for the dressing.
Peel the eggs, slice in half and place the yolks in a large mixing bowl and mash them with a fork. Dice the egg whites and set aside.
To the mashed egg yolks, add mayonnaise, dijon mustard, softened butter, vinegar, salt and pepper. Mix well to combine, then taste the dressing and add more salt if needed.
To the dressing, add potatoes, chopped egg whites, celery, green onion, and sweet relish. Gently stir with a spatula to combine then cover and chill in the fridge for at least half an hour.
Transfer to a serving bowl, garnish with a sprinkle of paprika or smoked paprika and chopped green onions or chives if desired.