How to Make It
Place potatoes, water, and 2 tablespoons of the salt in a large saucepan; bring to a boil over high. Reduce heat to medium-high; simmer, uncovered, until potatoes are fork-tender, about 10 minutes. Drain; chill 10 minutes.
While potatoes simmer, coarsely chop 3 of the eggs; transfer to a large serving bowl. Cut remaining 3 eggs in half; scoop yolks into a small bowl. Coarsely chop egg whites; add to chopped eggs in large bowl. Add mayonnaise, parsley, relish, mustard, vinegar, hot sauce, and remaining 3/4 teaspoon salt to yolks in small bowl; stir until combined and smooth.
Transfer chilled potatoes to chopped eggs in large bowl; add mayonnaise mixture and celery. Stir gently to combine. Garnish with paprika.