In a large mixing bowl, beat the softened butter and confectioner's sugar together until light and fluffy, about 2-3 minutes.
Add the vanilla extract and mix until well combined.
In a separate bowl, sift together the all-purpose flour and cornflour.
Gradually add the dry ingredients to the creamed butter mixture, mixing just until the dough comes together. Be careful not to overmix.
Cover the dough and refrigerate for at least 30 minutes, or up to 24 hours.
Preheat your oven to 350°F (180°C). Line a baking sheet with parchment paper.
Scoop rounded teaspoons of dough and place them about 2 inches apart on the prepared baking sheet.
Bake for 12-15 minutes, or until the edges are lightly golden.
Remove the biscuits from the oven and let them cool completely on the baking sheet before serving.