Pre-heat oven to 180°C (160°C fan-forced). Line 18 muffin holes with paper cases.
Place butter, sugar and vanilla in the bowl of an electric mixer. Beat until pale and creamy. Add eggs one at a time, mixing until well incorporated.
Fold in the flour, baking powder and milk alternately, mixing until batter is smooth. Spoon between paper cases and bake for 18-20 minutes. Allow to cool before frosting.
To make the frosting, beat the butter with an electric mixer until pale and fluffy. Add the vanilla, sugar and milk and beat until smooth. Add a little more sugar or milk a drop at a time to adjust the consistency. Pipe or spread onto cupcakes.