Preheat your oven to 170°C. Grease a 20cm square baking tin and line the base with baking paper.
Place the milk and butter in a small saucepan over a medium heat. Stir until the butter has melted, then set aside.
Whisk the eggs and castor sugar together until pale and thick. Add the lemon rind and the melted butter mixture. Sift in the flour, baking powder and salt and mix to combine.
Pour the batter into your prepared tin and bake for 25-30 minutes or until an inserted skewer comes out clean. Leave to cool completely before removing from the tin.
To make the lemon icing: soften the butter in the mixer / using handheld beaters. Sift in the icing sugar and add the lemon rind and juice. Mix again until you have a thick icing. Add the milk and beat until everything is combined and you have a spreadable icing. (Add additional milk if it is too thick.)
Spread the lemon icing over the top of the cooled cake. Cut into squares and serve. (Optional: decorate the squares with icing flowers/decorations.)