Place eggs in single layer in large pot. Fill pot with cold water until eggs are covered by about 1". Bring eggs, uncovered, to a rolling boil.
Remove pot from heat after boil is achieved and cover tightly with lid. Set timer and allow eggs to sit, covered, 13 minutes.
Carefully remove eggs from pot and place in bowl of ice water to cool and let cool completely, then remove shells.
Cut top 1/3 of eggs in a jagged pattern to create the top "shell" and gently pull out yolks. Rinse out egg whites.
In a bowl combine egg yolks, mustard, water, oil, paprika, salt and pepper; stir until smooth; spoon into piping bag. Pipe egg yolk mixture into egg white bottoms.
Place egg tops on piped egg yolks to create the top "shell". Insert 2 small carrot pieces in egg yolk mixture to create beak. Insert 2 peppercorns in egg yolk mixture to create eyes. Insert 2 small carrot pieces in the top "shell" (use small knife to slit egg to make it easier).
Put on a surface that will keep your chicks upright (we used napkin rings).
One Last Thing
I like to set things up like an assembly line so the children can help out with the simple stuff while I tackle the more complicated steps like creating the zig zag pattern on the egg tops.