Place the cubed potatoes in a large pot and cover with cold water by at least 1 inch. Add a generous amount of kosher salt to the water (it should taste pleasantly salty like light broth). Bring to a boil over high heat, then reduce to a steady simmer.

Cook potatoes for 12 to 15 minutes, until fork-tender but not falling apart. A paring knife should slide in easily with slight resistance. Drain in a colander and let steam-dry for 5 minutes.

While the potatoes cook, whisk together the mayonnaise, yellow mustard, apple cider vinegar, sugar, salt, black pepper, and garlic powder in a large mixing bowl until smooth and well combined. Taste and adjust seasoning as needed.

While the potatoes are still warm, transfer them to the bowl with the dressing. Gently toss to coat — warm potatoes absorb the dressing more effectively than cold ones, which builds flavor from the inside out.

Add the chopped hard-boiled eggs, diced celery, red onion, sweet pickle relish, and chopped parsley. Fold everything together gently with a rubber spatula until just combined. Be careful not to over-mix — you want distinct potato chunks, not a mash.

Cover the bowl tightly with plastic wrap and refrigerate for at least 2 hours, or ideally overnight. The flavor improves significantly as it chills.

Before serving, give it a gentle stir and taste for seasoning — add a pinch more salt or a splash more vinegar if needed. Transfer to a serving bowl, garnish with smoked paprika and fresh parsley, and serve cold.