Using an electric whisk, cream the butter and sugar until fluffy. Gradually add plain flour and cornflour, whisking until well blended.
Using a heaped teaspoon for each biscuit, roll into balls with floured hands to prevent sticking. Place on a baking tray lined with baking paper, about 2 to 3cm apart. Gently press down on each biscuit with a floured fork, then place a halved glace cherry in the centre.
Bake at 150 degrees C for 20 minutes or until bottoms are lightly browned. Cool for 5 minutes before moving from baking tray to wire racks.