1 1/4 teaspoons kosher salt plus more
1/2 cup mayonnaise
1/4 cup sweet pickle juice from jar
8-10 sweet-pickle chips
1 1/2 tablespoons Dijon mustard
1 teaspoon sugar
1/4 teaspoon freshly ground black pepper plus more
5 large hard-boiled egg yolks
2 tablespoons chopped red onion
2 tablespoons chopped flat-leaf parsley
Paprika
Place potatoes in a large pot. Add water to cover by 2", season with salt, and bring to a boil. Reduce heat to medium and cook until potatoes are tender when pierced with a knife, 20-30 minutes. Drain. Place potatoes in a large bowl and let cool slightly. Meanwhile, whisk mayonnaise, pickle juice, Dijon mustard, sugar, 1/4 teaspoon pepper, and 1 1/4 teaspoons salt in a small bowl for dressing. Using a large wooden spoon, coarsely smash potatoes, leaving some larger pieces mixed with some well-mashed pieces. Add dressing and egg yolks to potatoes and toss to coat, coarsely smashing egg yolks. Add onion and parsley; gently mix to incorporate. Season to taste with more salt and pepper, if desired. DO AHEAD: Can be made 1 day ahead. Cover and chill. Divide potato salad among small paper cups or bowls; dust with paprika. Top each serving with a pickle chip.