Place the potatoes in a large pot, and add cold salted water to cover them. Bring to a boil over medium-high heat. Boil, stirring occasionally, for 12–15 minutes, until just fork-tender (do not overcook, or they will fall apart). Drain the potatoes, and spread them out on a baking sheet. Let cool completely, about 15 minutes.

Meanwhile, place the eggs in a medium pot, and add cold water to cover them. Bring to a boil over medium-high heat. Cover the pot, and remove it from heat. Let the eggs stand in the covered pot for 10 minutes. Uncover, and transfer the eggs to a bowl filled with ice water. Let them cool completely, about 5 minutes.

Peel the cooled eggs. Cut 2 of the eggs in half lengthwise; place in an airtight container, and place in the refrigerator until ready to serve. Cut the remaining 6 eggs in half lengthwise; scoop the yolks into a large bowl, and set the whites aside. Mash the yolks with a fork. Add the mayonnaise, relish, mustard, vinegar, smoked paprika, garlic powder, salt, and pepper; whisk until smooth and creamy. Season with additional salt and pepper to taste.

Roughly chop the reserved egg whites from the 6 halved eggs. Add the chopped egg whites, cooled potatoes, onion, celery, and chives to the dressing. Gently fold everything together until well coated. Season with additional salt and pepper to taste. Cover and refrigerate for at least 2 hours or up to 12 hours for the flavors to develop.

Transfer the egg salad to a serving bowl or platter. Arrange the reserved halved eggs on top. Garnish generously with additional smoked paprika and chives. Serve cold.