Preheat oven to 180°C. Line a large baking tray with baking paper.
Using an electric whisk, beat butter, icing sugar and vanilla in a bowl for 5 minutes or until pale and creamy. Sift flour and cornflour together over butter mixture, and stir to form a soft dough.
Transfer mixture to a piping bag fitted with a 1.5cm fluted nozzle. Pipe 4cm-diameter swirls onto tray, leaving 3cm between each. Bake for 12-15 minutes or until light golden. Transfer to wire racks to cool completely.
To make the coffee filling, use an electric whisk to beat all the ingredients in a bowl for 5 minutes or until smooth and creamy. Spread filling onto half the cooled biscuits and sandwich with remaining biscuits to serve.