Preheat the oven to 375°F. Line baking sheets with parchment paper.
In a large bowl or stand mixer, cream together the butter, sugar, and lemon zest until light and fluffy, about 1-2 minutes.
In a separate bowl, whisk together the flour, cornstarch, and salt. Gradually add the dry ingredients to the butter mixture and mix on low speed until fully incorporated.
Scoop rounded tablespoon-sized balls of dough and place 1 inch apart on the prepared baking sheets. Gently flatten each cookie slightly with the bottom of a glass.
Bake for 8-10 minutes, until the edges are just starting to lightly brown. Let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
To make the lemon icing, whisk together the powdered sugar and lemon juice until smooth. Spread the icing over the cooled cookies. If desired, garnish with additional lemon zest.
Allow the icing to set completely before serving. Enjoy!
