Carefully lower eggs into a pot of gently boiling water. Cook for 12 minutes.

Transfer the eggs immediately to an ice water bath and let them cool for 10 minutes. Peel the eggs.

Slice the top third off of each egg crosswise to create a 'hat'.

Gently scoop the cooked yolks out of the bottom sections into a mixing bowl. Shave a tiny piece off the bottom of the egg whites if they don't stand upright.

Mash the yolks thoroughly with a fork until very fine. Stir in mayonnaise, mustard, vinegar, salt, and pepper until perfectly smooth.

Transfer the yolk mixture to a piping bag. Pipe generously into the hollowed bottom egg whites, mounding the filling high.

Place the top egg white pieces onto the filling at an angle to look like hatching shells.

Use tweezers to place two tiny olive pieces for eyes and a carrot triangle for a beak on the exposed filling of each chick.

Arrange on a platter lined with lettuce and keep refrigerated until serving.