Cut the red potatoes into 1 1/2″ to 2″ chunks, leaving the skin on for added nutrients. Boil the potatoes and eggs in a medium pot of water for 15 minutes or until the potatoes are fork-tender. Drain and cool under running water.
While the potatoes and eggs are cooking, dice the celery and red onion, placing them in a large mixing bowl. In a separate bowl, combine the sour cream, mustard, melted butter, salt, paprika, and pepper to create the dressing.
Cut the cooled potatoes into smaller 1/2″ pieces and add to the bowl with celery and onion. Peel and dice the eggs and add them to the bowl. Pour the dressing over the salad and toss to coat evenly. Serve immediately or store in the refrigerator.