Put the peanuts in a small baking pan and toast in a preheated 350-degree F oven 5 minutes, or until the skins start to crack. Cool slightly. Rub in a kitchen towel to remove the skins; chop coarsely.
Cut the potatoes into quarters and place in a baking pan. Toss with the olive oil, salt and several grindings of pepper. Bake in a preheated 375-degree F oven 30 minutes or until tender. Stir occasionally. Remove from the oven, toss with the vinegar and cool.
Place the diced red onion in a small bowl and cover with ice-water. Let sit 20 minutes to reduce the acidity. Drain and squeeze out the excess moisture with a paper towel. Bring a small pan of water to a boil, add the carrots and time for 2 minutes. Drain and rinse with cold water to stop the cooking. Pat dry.
Combine the cooled potatoes, onion, carrots and celery in a large bowl. Stir together the mayonnaise, yogurt, cilantro, mustards, cumin and several grindings black pepper. Combine with the vegetables and refrigerate. Stir in the peanuts just before serving.