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Beat the butter and sugar with an electric whisk for 4 mins until light and fluffy. Beat in the eggs, one at a time, then add the vanilla. Whisk in the cornflour and plain flour until the mixture comes together into a dough. Put the dough between two pieces of baking parchment, and roll out to a 6mm thickness using a rolling pin. Chill for 30 mins.
Heat the oven to 200C/180C fan/gas 6. Peel the top layer of parchment off the dough and stamp out circles using a 6cm round cutter (or the shape of your choice). Re-roll any offcuts and continue stamping out rounds until all the dough is used. Transfer the cookies to a second large baking sheet lined with baking parchment, spacing them 2cm apart (you may need two sheets). Bake for 7-10 mins. Leave to cool on the sheet for 15 mins, then transfer to a wire rack to cool completely. Will keep in an airtight container for one week.