In the bowl of your stand mixer fitted with the paddle attachment mix the butter and powdered sugar together on medium speed until smooth. Add the lemon zest and lemon juice and mix well.
In another bowl, whisk together flour, cornstarch, and salt. Add the dry ingredients to the butter mixture and stir until combined.
Form the dough into a long log, 1-1/4 inch in diameter. Cut the log in half and wrap each log separately with a plastic wrap. Chill the logs for at least 2 hour or until they get firm.
Preheat the oven to 350˚F. Slice the log into 1/4-inch thick slices and place on to the prepared baking sheet. Bake for 12-15 minutes.
Let the cookies rest in a baking sheet for 2-3 minutes. When the cookies are still warm, roll them in powdered sugar. Transfer the cookies to a wired rack and cool completely.