Add potatoes to a large pot and cover with salted water. Bring to a boil over medium-high heat. Reduce heat to medium-low, and cook until easily pierced with a fork but still firm, 15 to 25 minutes. Drain potatoes, and set aside to cool.

Meanwhile, whisk the mayonnaise, yogurt, pickle brine, and Dijon mustard together in a large bowl until well blended. Peel and roughly chop 2 of the hard boiled eggs. Stir in chopped eggs, onion, and pickles.

When potatoes are cool enough to handle, peel and cut them into bite-sized pieces. Add potatoes to the bowl with the dressing, and gently toss to coat evenly.