Using a knife, carefully cut around the middle of your egg with a zigzag pattern, starting at the front and going all the way around. You should end up with a top and bottom piece, both with jagged-looking edges.
Carefully scoop the yolk out with the end of a spoon and place it in a medium sized bowl.
If you'd like your chicks' 'shells' to be colored, set the cut egg whites in cups filled with water and a few drops of the food coloring of your choice. The longer they sit, the more vibrant their color will be. When your ideal colors are achieved, drain them on paper towels.
Blend the mayo, mustard, and egg yolks together until they are thick and creamy. You may need less mayo than is called for in order to create a very thick mixture. If it's too thin, the weight of the egg tops will squish the filling out.
Scoop the mixture into the baggie and set it aside.
Carefully slice the carrot into 1/4 or slightly thinner circles. Take each circle and cut it evenly into 6 tiny pie-shaped wedges. You can also use the tips of baby carrots, sliced in half.
Take each egg bottom and slice a little off to allow it to stand upright on your platter.
Snip a corner off of the baggie containing the egg yolk mixture, about 1 inch wide.
Squeeze the egg yolk mixture into the egg bottoms, filling them to about an inch and a half to 2 inches above the edge of the egg white.
Carefully place your egg tops onto the yolk mixture. Don't squish them down, but do arrange it so that your chicks are well-balanced and won't fall over.
Place a wedge of carrot in the middle of the egg yolk mixture, between the top and bottom egg whites.
Dip a toothpick or the end of a chopstick into black food coloring and carefully create 2 eyes on each chick.
Keep refrigerated until ready to serve!