Place the eggs in a single layer in a saucepan and cover with cold water by about 1 inch. Bring to a full boil, remove from the heat, cover, and let stand for 11–12 minutes, until the yolks and whites are firm.

Transfer the eggs to a large bowl of ice water and cool for 10 minutes. Gently crack and peel each egg; pat dry.

Slice each egg lengthwise. Remove the yolks to a mixing bowl and arrange the 24 egg-white halves on a serving platter.

Mash the yolks with mayonnaise, Dijon mustard, apple cider vinegar, smoked paprika, salt, and black pepper until creamy and smooth.

Spoon or pipe the yolk mixture evenly into the 24 egg-white halves.

Cut 12 black olives lengthwise in half to make 24 spider bodies. Slice each of the remaining 24 olives lengthwise into 8 narrow strips to make spider legs.

Set one olive half, cut side down, in the center of each filled egg. Arrange four olive strips on each side so every spider has eight legs.

Keep refrigerated until serving. For best appearance, assemble the olive spiders shortly before placing the eggs on the party table.