Place the eggs in a large pot and cover with cold water. Bring to a boil over medium-high heat, then remove from heat, cover, and let sit for 12 minutes.

Drain the eggs and transfer them to a bowl of ice water. Cool for 5 minutes, then peel under running water.

Slice each egg in half lengthwise. Scoop the yolks into a mixing bowl and set the whites aside on a serving plate.

Mash the yolks with a fork. Add the mayonnaise, Dijon mustard, white vinegar, salt, and black pepper. Stir until smooth.

Spoon most of the yolk mixture back into the egg whites, leaving a small amount in the bowl.

Stir a few drops of black food coloring into the remaining yolk mixture until it turns dark. Transfer this dark mixture to a small piping bag or zip-top bag with a tiny corner snipped off.

Pipe a spiral of the dark mixture onto each filled egg half. Use a toothpick to drag lines from the center outward, creating a web pattern.

Slice each black olive into thin strips. Arrange four strips on either side of each egg half to form spider legs.