Bring 2 quarts water to a boil in a medium saucepan. Carefully add eggs to boiling water; boil 12 minutes. Remove eggs, and place in ice water to cool completely, about 15 minutes. Once completely cool, peel the eggs, and rinse under cold running water. Pat eggs dry.
Slice eggs in half lengthwise, and remove yolks. Using a plastic dough scraper, push the yolks through a fine wire-mesh strainer into a small bowl. Using a fork, stir in mayonnaise, olive liquid, and Dijon mustard until smooth. Place mixture in a piping bag, and pipe evenly into egg white halves. Garnish each with a small dollop of caviar and if desired, sliced olives.
