Slice eggs in half lengthwise. Place 2 of the yolks in a large resealable plastic bag and dispose the rest of the yolks. Reserve 8 of the egg white halves and coarsely chop the other 8. Place the chopped egg whites into the bag with the yolks and add the yogurt, relish, mustard, lemon juice, and salt. Combine the mixture with hands to fully combine the mixture.
Squeeze the mixture to one corner of the bag and slice off the corner. Squeeze the mixture into each of the 8 saved egg white shells. Sprinkle parsley leaves on top.