Place whole potatoes in a pot with 1/4 cup kosher salt. Cover with cold water and bring to a boil over high heat. Reduce heat to medium-low and simmer until tender, about 40 minutes.

Transfer the cooked potatoes to a plate and allow them to cool to room temperature. Once cooled, peel off the skin and cut into larger than bite-size pieces.

In a mixing bowl, combine the potato pieces, celery, onions, parsley, and chopped hard-boiled eggs, breaking up larger pieces of potato as you mix.

In another mixing bowl, whisk together mayonnaise, cider vinegar, mustard, salt, black pepper, and cayenne pepper until well combined.

Pour the mayonnaise mixture over the potato mixture and stir until well combined. Cover and refrigerate for 2 to 3 hours until completely chilled.

Before serving, taste the salad for seasonings and texture, adjusting with salt or mayonnaise as needed.