Place eggs in a pot of salted water. Bring the water to a boil, and let eggs cook in boiling water until they are hard boiled, approximately 10 to 15 minutes. Drain eggs, and let cool. Once cool, remove the shell, cut the eggs in half lengthwise and scoop out the yolks.
Place the yolks in a medium-size mixing bowl and mash them. Blend in vinegar, mayonnaise, mustard, salt and pepper. You may need to add more mayonnaise to hold the mixture together, but it should be slightly dry.
Carefully put the egg yolk mixture back into the egg whites but do not pack it. There will be enough mixture so the whites are overfilled. Sprinkle with paprika. Place on bed of lettuce and/or garnish with parsley. Cool before serving.