To make the lemon cookies: Preheat the oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a handheld mixer, beat the butter and powdered sugar together for 1 to 2 minutes or until well combined. Then, mix in the egg yolk, lemon juice, lemon zest.
Add the flour, cornstarch, and salt and continue mixing until fully combined. The cookie dough will be a little crumbly at first, but it will come together as you continue mixing it.
Using a one tablespoon cookie scoop, scoop the cookie dough, roll into a ball, and gently press down on each ball of cookie dough to flatten them slightly.
Bake for 11 to 13 minutes or until the top of the cookies are set. Remove from the oven and allow to cool on the baking sheet for 5 to 10 minutes, then carefully transfer the cookies to a wire rack to cool completely.
To make the lemon icing: Whisk the powdered sugar and 2 tablespoons (30 ml) of lemon juice together until well combined and no lumps remain. If the icing is too thick, add ½ teaspoon of lemon juice at a time until the icing has reached your desired consistency.
Evenly distribute the icing on top of all of the cookies. Allow the icing to harden slightly before serving.