Put the potatoes and two teaspoons of salt in a large pot and cover with cold water for about two inches. Bring to a boil over high heat, then reduce the heat and simmer until the potatoes are tender but not falling apart, about five minutes.
Meanwhile, stir the mayonnaise, Cherry Horseradish Sauce, mustard, vinegar, celery salt and cayenne together in a large bowl with 1/2 teaspoon salt and a few grinds of black pepper.
Stir in the hot potatoes and the celery, celery leaves and shallots.
Let cool to room temperature before stirring in the parsley and eggs. Season with salt and pepper. Refrigerate until ready to serve.