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.
Season to taste with salt and pepper, and slice the remaining hard boiled egg for a garnish on the potato salad. May be served immediately or chilled in the fridge.
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