Wash, peel (optional), and boil the potatoes until fork-tender. Drain, cool completely, and cut into bite-sized cubes.
In a large bowl, whisk together the mayonnaise, Dijon mustard, chopped fresh dill, salt, and black pepper.
Add the cooled potatoes, chopped celery, and diced red onion to the bowl.
Gently fold the ingredients until the potatoes are evenly coated with the creamy dill dressing.
Taste and adjust the seasoning with additional salt, pepper, or dill if desired.
Cover the bowl and refrigerate for at least 1 hour to allow the flavors to develop.
Serve chilled, garnished with extra fresh dill for a vibrant finish.