Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper. You will only need one baking sheet if you're using a large one.
In a food processor, pulse butter with powdered sugar until combined. Add cornstarch, extract, zest and flour; process until a soft dough forms.
Remove the dough to a floured surface and divide into 4 equal chunks. Roll a chunk of the dough into a skinny log about 12 inches long. Cut each log into 12 pieces, and roll each piece into a ball. Place the balls on the prepared baking sheet about 1 inch apart. They won't spread much, so you can probably get them all on one baking sheet.
Bake for 20 to 22 minutes, until the bottoms are golden but the tops are still light.
ROLLING SUGAR
In a medium bowl, mix powdered sugar and lemon zest. Just use a fork to blend in the zest and get that powdered sugar scented with lemon.
Add a few warm cookies at a time to the sugar mixture. Roll in the sugar and remove to a wire rack.
While still warm, use a toothpick to poke 4 little holes into the top of each cookie to make a buttonhole pattern. Cool completely on wire rack.
Notes
Cookies can be stored in an airtight container for up to 1 week.