Add the butter and sugar to a medium-sized mixing bowl or stand mixer and beat with an electric mixer until well mixed and smooth. Beat in the vanilla.
Sift in the flour, cornflour and salt and mix to a crumbly dough. Knead a few times to bring it together, then wrap in plastic wrap and refrigerate for 1 hour (or put in the freezer for 15 minutes) to firm it up slightly.
Preheat the oven to 350°F/180°C and line two cookie sheets with baking parchment paper.
Roll tablespoonfuls of the cookie dough into balls and place onto the cookie sheets, spacing them at least 1 inch apart.
Place into the oven and bake for 12 minutes or until the edges just begin to brown.
Allow to cool on the trays for a few minutes, then transfer to a wire rack and sift the remaining powdered sugar over them.
Store in an airtight container (with wax paper or baking parchment paper between layers) for up to 2 weeks.
Notes
You can use salted or unsalted butter in this recipe - it will work either way, just don't add additional salt if using salted.If the dough is too sticky to handle after chilling, you can refrigerate it for an additional 30 minutes before rolling it.Don't have cornstarch on hand? Use rice flour or tapioca flour instead.Add a teaspoon of cinnamon or pumpkin pie spice to the dough for a warmer flavored cookie.Add ½ cup of chopped dark chocolate or nuts to the dough for a different flavor and texture.Instead of powdered sugar, try sprinkling the tops of the cookies with melted white chocolate, crushed candy canes, or festive sprinkles.Change the flavor of the cookie by using almond, coconut, or maple extract instead of vanilla.