Place eggs in a single layer in a saucepan and cover with one inch of cold water. Bring to a boil.

Remove from heat, cover, and let stand for 12 minutes.

Transfer eggs to an ice water bath for 5 minutes, then peel carefully.

Slice a thin sliver off the bottom of each egg so they stand upright.

Cut the top third off each egg. Carefully remove the yolks from the bottoms and the top slices without breaking the whites.

In a small bowl, mash the yolks with mayonnaise, mustard, salt, and pepper until smooth and creamy.

Transfer the yolk mixture to a pastry bag fitted with a plain round tip.

Pipe the yolk mixture into the bottom egg whites, filling them high enough so the filling protrudes significantly above the rim.

Place the top egg white slice onto the piped yolk to form a hat.

Cut two small circles from the black olive for eyes and a small triangle from the carrot for a beak; press them into the yolk filling face.

Serve immediately or refrigerate.