Whisk together the butter and sugar with an electric mixer until light and fluffy then whisk in the vanilla extract.
Sift together the flour, cornflour and salt and add to the butter mixture. Stir until it starts to clump together.
Add the milk and mix to form a soft dough. If it seems like it will be too sticky to roll out then add a tablespoon of flour. Be careful not to add too much, the dough will firm up once it is chilled.
Knead the dough by hand very briefly, just until it is smooth.
Form it into a disc, wrap and refrigerate for at least 30 minutes, until it is firm enough to roll out. Line two baking sheets with baking parchment.
Roll the chilled dough out on a floured surface or between two sheets of baking parchment to about 5mm / ¼ inch thick.
Dip your cookie cutters in flour and cut out as many shapes as you can. Re-roll the trimmings and cut out more cookies.
Place the cookies slightly spaced apart on the baking sheets. Place the trays in the freezer for 15 minutes, or in the fridge for 30.
Meanwhile, preheat the oven to 180°C/160°C fan/350°F/ gas mark 4.
Bake the cookies for about 11 minutes for soft ones, until they are just turning pale golden around the edges. For crisp cookies, bake for about 15-20 minutes, until they are more uniformly golden brown.
Cool on the trays for a couple of minutes then transfer the cookies to a wire rack and allow to cool completely before decorating and storing.