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. Simmer until tender, about 40 minutes (depending on size). Transfer cooked potatoes to a plate. Allow them 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, chopped hard-boiled eggs. Combine ingredients, breaking up larger pieces of potato.
Place mayonnaise in mixing bowl. Add cider vinegar, mustard, salt, black pepper, and cayenne pepper. Whisk until well combined.
Pour mayonnaise mixture onto potatoes; stir until well combined. Cover and refrigerate until completely chilled, 2 to 3 hours. Taste for seasonings and texture. Salad may need a bit more salt and another spoonful of mayonnaise.
Choose potatoes of uniform size so cooking time is the same for all.
You can make the dressing while waiting for the boiled potatoes to cool. But remember, they absolutely must be room temperature before you dress them.
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