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Combine the butter and 6 tablespoons powdered sugar in a large mixing bowl and cream with an electric mixer on medium speed until very light and fluffy; this will take a couple of minutes.
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Add the vanilla and lemon zest and beat until combined.
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Sift the flour, cornstarch, and salt over the butter mixture. Beat on low speed until a cohesive dough forms, stopping to scrape the sides and bottom of the bowl a few times. (The dough will be crumbly at first but it will eventually come together.)
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Stir a few times with a rubber spatula to ensure all of the dry ingredients are incorporated, then cover the bowl and refrigerate for 1 or 2 hours.
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After the dough has chilled, preheat the oven to 350. Spray 2 large baking sheets with cooking spray.
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Shape the dough into 1-inch balls and arrange 2 inches apart on the baking sheets.
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Use the bottom of a flat-bottomed glass (or just use your palm) to flatten dough balls to 1/4-inch thickness. (If the glass sticks you can spray it lightly with cooking spray.) Don’t get the cookies too thin or they’ll burn!
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Bake 12 to 14 minutes, until the cookies look set all over. The cookies WILL NOT brown.
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Let the cookies sit for 1 minute on the baking sheets, then use a thin metal spatula (I use a large offset spatula) to transfer the cookies to a wire rack. Don’t use your fingers or the cookies will crumble.
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Sift the remaining powdered sugar over the tops of the cookies while they’re still warm. (You can do a second coat after the cookies cool if you want.) Serve.
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Cool cookies to room temperature before storing them—they don’t have to be room temp to serve them though!
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Uneaten cookies can be stored at room temperature in an airtight container, layered with wax paper, for about a week
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The cookies can also be frozen, also in an airtight container, for up to 3 months.