Bring a small pot of salted water to a boil. Carefully add eggs. Bring water to a simmer and cook eggs 10 minutes. Drain and transfer to a bowl of ice water; let sit until cool enough to handle. Peel.Meanwhile, whisk mayonnaise, celery, relish, scallion, mustard, 2 tsp. parsley, and 2 dashes hot sauce in a medium bowl; season with salt and pepper.Halve eggs lengthwise. Scoop yolks into mayonnaise mixture and place whites on a plate. Gently mash yolks into dressing; season with salt and pepper. Using 2 forks, fill egg halves with yolk mixture.Top eggs with pepper and more parsley and serve with hot sauce.

Do Ahead: Eggs can be made 1 day ahead. Cover and chill egg whites and filling separately; fill just before serving.