Place the caster sugar and an icing sugar in a food processor. Process until the sugars are very fine and free of lumps. If not using a food processor, simply sift the icing sugar into a bowl and mix together with the caster sugar.
Using a hand-held electric mixer, beat the butter at medium speed for 30 seconds. Add in the sugars in 3 batches, beating for 1 minute after each addition at medium speed and scrapping the sides occasionally. Add in the egg yolk, one at time, and beat at medium speed for 30 seconds and scrapping the sides after beating. Beat in the vanilla at low speed.
Scoop 1/3 of the batter into the Vanilla Dough flour and mix well. For the remaining 2/3 of the batter, add in 125 grams (1 cup) of the flour and the cocoa powder and mix well. Mix in more flour until it has the same consistency as the Vanilla Dough.
Reserve 1/5 of the Vanilla Dough for the eyes. Shape into a penguin shape using the same method as the Penguin Cookies. Roll 2 more chocolate logs and shape into ears.
Preheat the oven to 160 degrees Celsius. Slice the cookies into 1/8-inch thick and reshape them if necessary. Roll small balls of Vanilla Dough and place on the cookie and stick chocolate rice down as the eyes. Use chocolate rice to decorate if desired. Place them about 1-inch apart on a lined baking sheet and bake for 12 to 15 minutes. The cookies will expand during baking. Cool the cookies the baking sheet for 10 minutes, then transfer to a wire rack to cool completely before storing in an airtight container.