In a medium bowl, whisk together the flour, cornstarch, and salt. Set aside.
In a large mixing bowl, beat the softened butter and powdered sugar on medium speed for approximately two minutes until smooth and creamy.
Add the vanilla extract and mix until combined.
Gradually add the dry ingredients, mixing on low speed until a soft dough forms.
Divide the dough into two equal portions. Shape each into a log about six inches long and 1¾ inches in diameter.
Wrap the logs tightly in plastic wrap and refrigerate for at least one hour.
Preheat the oven to 325°F (163°C). Line two baking sheets with parchment paper.
Slice each dough log into approximately 18 cookies, about ⅓ inch thick.
Arrange the cookies one inch apart on the prepared baking sheets.
Bake for 15 to 18 minutes per batch, until the edges and bottoms are lightly golden.
Let the cookies cool on the baking sheet for five minutes before transferring them to a wire rack.
Cool completely before serving or storing.