Place potatoes in a large pot of cold salted water and bring to a boil. Once boiling, carefully add eggs to the same pot—this is efficient since both need similar cooking times. Boil for 12-15 minutes until potatoes are fork-tender and eggs are hard-cooked. While they cook, prepare your mise en place by finely dicing the onion into small pieces and cutting celery into 1/8-inch pieces for a subtle crunch that won't overpower the salad.
Drain potatoes and eggs together, then immediately transfer to a bowl of ice water to stop the cooking process and cool them quickly—this prevents the potatoes from becoming mushy. Once cooled, peel the eggs under cool running water, which makes the process much easier. Separate 3 egg yolks and set aside; set the remaining whole eggs and whites aside for chopping.
In a medium bowl, whisk together mayonnaise, Dijon mustard, vinegar, and salt. I always use Hellmann's mayo because it gives the creamiest, most flavorful base, and Grey Poupon mustard for that sharp, authentic deviled egg kick. Mash the reserved 3 egg yolks with a fork until smooth, then whisk them directly into the dressing mixture until fully incorporated and creamy. Taste and adjust seasoning with additional salt and black pepper as needed.
Chop the remaining 7 eggs (whites and any whole eggs) into bite-sized pieces. Cut cooled potatoes into 1-inch cubes—this size is substantial enough that the potato salad has texture but small enough that each bite contains potato, egg, and dressing. In a large mixing bowl, combine the chopped eggs, diced onion, diced celery, and potato cubes.
Pour the deviled egg dressing from Step 3 over the potato and egg mixture, then fold everything together gently but thoroughly using a spatula or large spoon, making sure every piece is coated. I like to do this folding action rather than stirring to keep the potatoes and eggs intact instead of breaking them into smaller pieces. Taste and adjust seasoning with additional salt and black pepper if needed.
Transfer the salad to a serving bowl or platter and top with fresh chopped dill and a generous sprinkle of smoked paprika, which adds a nice depth of flavor beyond regular paprika. Serve immediately, or refrigerate until ready to serve. The salad actually tastes better after 1-2 hours as the flavors meld together.