To prevent cracking, remove eggs from refrigeration about 30 minutes prior to boiling. Place eggs in a saucepan and cover with cold water. Bring to a boil then let simmer for approximately 6 minutes. Eggs will be done if you can spin them on their vertical axis. (If they fall to the side, they're not done). Remove from water and place in an ice bath (water and ice) several times until they have cooled (you can also make hours ahead and refrigerate).
Peel the eggs and rinse off any remaining shells. Cut the top 1/4 off of the egg and gently scoop out the yolk using a small knife or spoon. Add the yolk to a bowl, mash with a fork and place egg white on a serving platter. (if using a flat platter, cut a small piece off of the bottom of the egg so that it sits flat). Add mayonnaise and mustard to the egg yolks and mix well. Carefully fill the bottom portion of the egg white with the yolk filling. Next, place the white "cap" on top of the egg yolks. Cut the black olive into 12 pieces and place 2 pieces for the eyes. Cut the carrot into 12 small pieces and put a piece on the yolk for the nose. Refrigerate until ready to serve. Makes 8.