Place whole potatoes in a pot with 1/4 cup kosher salt. Cover with cold water. Bring to a boil over high heat. Reduce heat to medium-low and simmer until tender, about 40 minutes (depending on size). Transfer cooked potatoes to a plate and allow to cool to room temperature.

When potatoes are completely cooled, peel off the skin. Cut into larger than bite-size pieces as the pieces will break down slightly when you toss with the dressing. Transfer potato pieces to a mixing bowl. Add celery, onions, parsley, and chopped hard-boiled eggs. Combine ingredients, breaking up larger pieces of potato.

Place mayonnaise in a mixing bowl. Add cider vinegar, mustard, salt, black pepper, and cayenne pepper. Whisk until well combined.