In a medium bowl, sift together flour, cornstarch, and salt. Set aside.
In a mixer bowl fitted with the paddle attachment, beat the butter on medium speed for 30 seconds until creamy. Add powdered sugar and beat for about 2 minutes until smooth. Beat in vanilla extract. Add flour mixture and beat on low speed just until combined. Do not over mix.
If the dough is soft, chill in the refrigerator, covered, for 1-2 hours until firm so that cookies will spread as little as possible while baking.
Preheat oven to 350F/180C. Line 2 pans with parchment paper.
If cookie dough is hard to handle after refrigerating, leave on the counter for a few minutes to soften.
Using an ice cream scoop or level tablespoon, drop rounded balls of dough, 1 inch/2.5cm in diameter, onto prepared baking sheets. Bake for 10-12 minutes, until cookies just begin to brown at the edges. Leave to cool for 10 minutes. Then, while they are still warm, gently roll them in powdered sugar, careful not to cause them to crumble. Transfer to a wire rack to cool completely. Once cooled, roll them one more time in powdered sugar if desired.
Cookies will keep well for a few days at room temperature in an airtight container, or they can be frozen for up to a month.