Put half the butter and all the sugar in a bowl. Using an electric whisk or wooden spoon, beat together until smooth and creamy. Beat in the egg and half the vanilla extract until thoroughly combined.
Tip the flour into the mixture and mix on a low speed until it comes together to form a dough. Gather up into a ball, wrap in cling film and chill in the fridge for 20 mins.
Heat oven to 180C/160C fan/gas 4. Line 2 baking trays with baking parchment. Put the biscuit dough on a lightly floured surface and roll out until about 5mm thick. Cut out the biscuits using a 6cm round cutter. Transfer the biscuits to the prepared trays and insert the lolly sticks into the sides, just a quarter of the way through. Bake for 6-7 mins until the edges are golden brown, then carefully transfer to a wire rack and allow to cool completely before decorating.
Meanwhile, make some buttercream frosting. Place the remaining softened butter in a bowl and beat with a wooden spoon. Slowly add the icing sugar, 1 tbsp at a time, until thoroughly incorporated and you have a smooth, creamy mixture. Add a little milk and the remaining vanilla extract with a few drops of food colouring to give a pale yellow colour. Chill for 5 mins.
Put the desiccated coconut in a small bowl, add a few drops of yellow food colouring and mix well until the coconut is coloured pale yellow.
Spread the buttercream frosting over one side of the biscuit and sprinkle with the coconut. Add 2 chocolate chip eyes to each. Pinch a little orange fondant icing and shape into a beak and press into the mixture. Decorate with a ribbon, if you like, and serve. Will keep for 2 days in an airtight container.