Place butter and sugar in the bowl of a large stand mixer, fitted with a paddle attachment OR in a large mixing bowl with a wooden spoon. Mix on medium speed or by hand until creamy, about 2 minutes. Add egg and vanilla, beating well until smooth.
In a separate medium bowl, combine flour, cornstarch, baking powder, and salt. Fold into butter mixture until dough is just combined.
Scrape dough into a ball and wrap in plastic wrap. Refrigerate dough at least 1 hour or up to 3 days.
When ready to bake cookies, preheat oven to 350F. Line two baking sheets with parchment paper and set aside.
Remove dough from fridge and use a medium cookie scoop to scoop dough out into 1-in balls. Place balls 2 inches apart on prepared baking sheets and flatten cookies slightly.
Bake cookies at 350F 10-12 minutes until edges of cookies are golden-brown. Allow cookies to cool on pan 10 minutes, then transfer to a wire cooling rack to cool completely.