In a large bowl, combine the cooked potatoes, hard-boiled eggs, shredded carrot, chopped celery, and diced onion. Use your spoon to gently chop up the eggs right in the bowl with the potatoes.
In a separate bowl, whisk together the mayonnaise, yellow mustard, vinegar, sugar, paprika, and salt until smooth.
Pour the dressing over the potato mixture and stir gently to combine. As you mix, go ahead and mash some of the potatoes with your spoon—this helps create that creamy texture while still keeping some chunks for a nice bite.
Cover the bowl and refrigerate for at least 2 hours, or even better, overnight to let all those flavors blend beautifully.
Right before serving, sprinkle a little extra paprika on top for a pop of color and flavor.