Peel, quarter-cut and place potatoes in a kettle with enough lightly salted water to completely cover them; bring to a boil over high heat; cook ~15 minutes, until a potato piece easily breaks apart when a fork is inserted.
Remove from heat and drain; let cool; when cool to the touch, cut all into ~½ inch cubes.
For easy-peel, perfectly yellow yolk, hard boiled eggs: place eggs in an empty kettle; fill with cold tap water until eggs are covered by 1+ inch of water. Place on high heat and bring to a rolling boil; time boil for 2 minutes. Remove from heat and cover for 23 minutes; drain and place in ice water bath; when cool, peel and slice each egg.
In a large mixing bowl, layer the cubed cooked potatoes, salt and pepper, onion, celery, and 3 of the 4 sliced eggs; cover and refrigerate up to 24 hours.
Mix all dressing ingredients in a small mixing bowl; thin dressing with 1 additional tablespoon half & half at a time until it reaches the consistency of syrup.
Just before serving, gently fold the dressing mixture into the potato salad.
Transfer to a serving bowl; arrange remaining egg slices on top of the salad; garnish with parsley.
