Fill a large pot with salted water and bring to a boil. Gently add in red potatoes and boil until for tender, approximately 5-7 minutes, though depending on size of potatoes, it could take slightly longer. When tender, drain.
While potatoes are cooking, whisk together the mayonnaise, plain Greek yogurt, mustard, apple cider vinegar, garlic powder, onion powder, lemon pepper, dried basil and salt in a medium size bowl. Set aside, ready to use when potatoes are finished cooking.
In a large bowl combine cooked red potatoes, celery, pickles and hard boiled eggs. Pour mayonnaise mixture in with potatoes. Stir until everything is throughly combined.
Top with chopped parsley, green onions or chives if desired. Refrigerate at least 2 hours prior to serving, unless you enjoy warm potato salad (some do!).