Combine the flour, baking soda, salt, and corn starch in a medium bowl and whisk together. Set aside.
In the bowl of a standing mixer, add the room-temperature butter and granulated sugar. Cream on low speed until light and fluffy. Add the lemon zest and juice, egg, and vanilla. Mix until just combined, scraping down the sides as needed.
Add the flour mixture to the butter mixture in the bowl of the standing mixer. Beat on low just until the dough is combined, scraping the sides as needed. The dough will be thick and sticky.
Cover the dough and refrigerate for at least 3 hours (and up to 3 days). Do not skip this step, or the cookies will not work.
After the dough has been refrigerated, preheat the oven to 350 degrees Fahrenheit. Line a large baking sheet with parchment paper.
Using a medium size cookie scoop (about 2 tablespoons), roll the dough into balls. As you scoop each ball, roll it in the powdered sugar before placing it on the prepared baking sheet. Note: if the dough has been refrigerated for more than 3 hours, you may need to let it rest at room temperature for 5 to 10 minutes before scooping so it is easier to handle.
Bake the cookies for 10 to 12 minutes or until the edges look set. The middle, between the crinkles, might still look sticky, but that's fine. (If you are cooking them in batches, place the unused dough in the fridge until you are ready to cook the next batch - the dough works best if it stays cool).
After baking, let the cookies rest on the baking sheet for 5 minutes before removing them to a wire rack to continue cooling. The cookies will deflate and look more "crinkly" as they cool.