Place eggs in a large saucepan, cover eggs with cold water, and bring to a boil. Cook 2 minutes. Cover pan and remove from stove. Allow to sit at room temperature until water has completely cooled.
Peel eggs under cold water and slice in half lengthwise. Carefully remove yolk and place in small mixing bowl. Reserve cooked egg whites. Mash yolks. Add mayonnaise, mustard, salt, and pepper together.
Optional: Add pickle relish if using. I love the relish and truly believe Grandma made hers this way. However my sister believes this was not in Grandma's recipe.
Spoon yolk mixture into egg white shells and sprinkle with paprika. Chill and serve cold.