Cool and peel the eggs before halving, then lift the yolks gently into their bowl. Set the white halves on a stable plate with their hollows upward. Mash the filling until smooth before dividing it among all twelve; distributing it first makes it easier to correct uneven mounds without repeatedly handling the finished olive eyes.
Cut the olives crosswise so the pimiento centers show. Press a half into each mound with its cut face upward, without forcing it through the filling. Keep the eggs covered and refrigerated until service as directed. Put out a smaller serving plate if the rest are not needed immediately, and keep the unused portion cold rather than leaving the entire prepared batch on a warm table.
Timing and servings are estimates. Equipment, ingredients and portion sizes affect the result.