Peel and dice the potatoes, then boil them in salted water until fork-tender (about 10-12 minutes). Drain and let them cool.
Boil eggs for 10 minutes, then cool, peel, and dice them.
Finely chop the cucumber, radishes, celery, and chives.
In a mixing bowl, whisk together mayonnaise, sour cream, mustard, salt, and black pepper.
Gently fold the cooled potatoes, eggs, and chopped veggies into the dressing.
Mix well but avoid mashing the potatoes—keep them chunky.
Cover and refrigerate for at least 30 minutes to let flavors meld.
Serve chilled, garnished with extra chives.