Preheat your oven to 180°C (350°F).

In a mixing bowl, cream together the caster sugar and room-temperature butter or margarine using an electric mixer until light and fluffy.

Add the large eggs one at a time, mixing well after each addition.

Gradually add the self-raising flour and mix on low speed until just combined.

Incorporate the milk and vanilla essence into the dough, mixing gently.

Add a few drops of green food coloring and mix until the color is consistent throughout.

Portion out the dough using a spoon or cookie scoop onto a baking tray lined with parchment paper.

Bake in the preheated oven for about 10-12 minutes, or until the edges start to turn lightly golden.

Remove the tray from the oven and allow the cookies to cool for a few minutes before transferring them to a wire rack.

Mix additional softened butter with icing sugar and vanilla essence until creamy and spreadable.

Once cookies are cooled, spread or pipe the icing on top of each cookie, and consider adding ready-to-roll icing shaped like shamrocks.