Place eggs in a single layer in a stainless steel saucepan. (Do not use nonstick.) Add water to depth of 3 inches. Bring to a rolling boil; cook 1 minute. Cover, remove from heat, and let stand 10 minutes. Drain.
Place eggs under cold running water until just cool enough to handle. Tap eggs on the counter until cracks form; peel.
Slice eggs in half lengthwise, and carefully remove yolks. Mash together yolks, yogurt, and next 6 ingredients until smooth using a fork. Spoon yolk mixture into egg white halves. Top with pickled okra slices. Serve immediately, or cover and chill 1 hour before serving.