In large pot, cook potatoes over high heat using 1 tablespoon of salt added to just enough water to cover the potatoes. Boil until tender when pierced with a knife. Drain. Half or quarter potatoes as desired and set aside.
Hard boil eggs and cool. Peel and dice 2 of the eggs into 1/4 inch cubes. Slice the 3rd egg into 1/4 inch rounds and set aside for the garnish.
Combine diced egg, mayonnaise, celery seed, mustard, 2 teaspoons of salt and black pepper in a large bowl and whisk to combine.
Add reserved potatoes to mayonnaise mixture. Add celery, red pepper, carrot, pickle, green onions and chopped parsley. Stir to combine.
Chill for 30 minutes or longer. Garnish with paprika and reserved hardboiled egg slices.