Lemon Meltaways

For the cookies: In a medium bowl, whisk together the flour, cornstarch, and salt; set aside.

In the bowl of a stand mixer fitted with the paddle attachment, combine the powdered sugar and lemon zest. Mix on low speed for 1 minute. The sugar will start to clump as the lemon zest releases its oil. Add the butter and beat on medium speed until light and fluffy, 3 to 5 minutes. Scrape down the sides of the bowl with a rubber spatula and beat in the vanilla. Reduce the speed to low and slowly add the flour mixture, mixing until just combined, about 1 minute. Give a final stir with the spatula to make sure there are no visible traces of flour.

Transfer the dough to a large piece of plastic wrap and roll into a log approximately 1 1/4 inch in diameter. Wrap the log in the plastic, twisting the ends closed. Refrigerate until cold and firm, at least 1 hour and up to 12 hours.

Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.

Unwrap the log and cut into 1/4-inch-thick rounds. Place the rounds on the prepared baking sheets, spacing them about 1 inch apart (they can be closer together since they do not spread while baking).

Bake the cookies, rotating the pans halfway through, until they are set and barely golden on the bottom, 11 to 13 minutes. Transfer the cookies to a cooling rack and allow them to cool completely.

For the glaze: Meanwhile, place the sugar in a small bowl and whisk in the lemon zest and 2 tablespoons lemon juice, adding more lemon juice a little at a time as necessary until the glaze reaches a spreadable consistency. Spoon a small amount of glaze onto each cookie, using the back of the spoon to spread evenly over the top. Let the glaze set before serving, about 1 hour.