In a mixing bowl, beat 1 cup of softened unsalted butter with ½ cup of powdered sugar using an electric mixer on medium speed until light and fluffy, about 2-3 minutes.

Lower the mixer speed and add 1 tablespoon of lemon zest, 2 tablespoons of fresh lemon juice, and 1 teaspoon of vanilla extract to the butter mixture. Mix until just combined, about 30 seconds.

In a separate bowl, whisk together 2 cups of all-purpose flour, ¼ cup of cornstarch, and ¼ teaspoon of salt until evenly combined.

Gradually add the dry flour mixture into the butter mixture, mixing on low speed until just combined.

Divide the dough into two equal portions and shape each into a log approximately 2 inches in diameter. Wrap the logs in plastic wrap and refrigerate for at least 1 hour.

Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper.

Once the dough is firm, carefully slice each log into ¼-inch thick rounds and place on the prepared baking sheets about 1 inch apart.

Bake the cookies in the preheated oven for 10-12 minutes. They should be just golden at the edges and pale in the center.

Let the cookies cool on the baking sheets for about 5 minutes, then transfer them to a wire rack.

While the cookies are still warm, coat them with powdered sugar using a fine sieve.

For an optional second sprinkle of powdered sugar, wait until the cookies have cooled completely.