Boil the eggs: Place the eggs in a single layer in a saucepan and cover with cold water by an inch. Bring to a boil over medium-high heat, then cover, remove from heat, and let sit for 10-12 minutes.

Cool in ice water: Transfer the eggs to a bowl of ice water and let them sit for 5 minutes. This stops the cooking and makes the shells easier to remove.

Peel the eggs: Gently crack each shell all over and peel under cool running water, starting at the wider end where the air pocket sits. The shells should come off in large, clean pieces.

Halve and scoop yolks: Slice each egg in half lengthwise and gently pop the yolks out into a medium bowl. Set the whites aside on a plate, cut side up.

Mash the filling: Mash the yolks with a fork until no large lumps remain. Add the mayonnaise, mustard, vinegar, salt, pepper and smoked paprika, then stir until smooth and creamy.

Taste and adjust: Taste the filling and add a little more salt, pepper or mustard if needed. The mixture should be thick enough to hold its shape when piped.

Fill the egg whites: Spoon the filling into a piping bag or a zip-top bag with the corner snipped off. Pipe the mixture into the egg white halves, mounding it slightly above the rim.

Dust with paprika: Sprinkle a light dusting of smoked paprika over the filled eggs for color and a faint smoky flavor.

Build the spiders: Press one small round olive slice into the center of each egg for the spider body, then arrange 4-6 thin olive slivers around it to look like legs.

Garnish and chill: Scatter a few chopped chives around the platter if using, then refrigerate the eggs for at least 15 minutes before serving so the filling firms up.