01 - Place eggs in a saucepan and cover with cold water. Bring to a boil, then cover, remove from heat, and allow eggs to stand for 10 minutes.
02 - Drain hot water and rinse eggs under cold running water until completely cool. Peel shells carefully to avoid tearing the egg whites.
03 - Using a sharp knife, slice each egg in half lengthwise. Gently remove yolks and transfer to a mixing bowl. Reserve the egg white halves.
04 - Mash cooked yolks thoroughly with mayonnaise, Dijon mustard, vinegar or lemon juice, salt, black pepper, and smoked paprika until the mixture is creamy and smooth.
05 - Evenly spoon or pipe the yolk mixture into the hollowed egg whites, mounding slightly for presentation.
06 - Slice each olive in half. Use one half as a spider body and slice the other half into thin strips to form legs.
07 - Place one olive half body atop each filled egg. Arrange three to four olive leg strips on each side of the body to resemble spider legs.
08 - Lightly dust eggs with additional smoked paprika for garnish. Chill until serving.