• Put the softened butter and sugar in the bowl of a stand mixer and beat with the paddle attachment until light and creamy. If you want the cookies to be more lemony, add a teaspoon of lemon zest in with the butter and sugar.
• Whisk together flour and cornstarch. If your flour is lumpy you can sift it, but whisking should be fine. Add to the mixing bowl and beat on medium speed until a soft dough forms.
• Using a small cookie scoop, scoop out about 4 dozen balls or spoon out 6 dozen if you want smaller cookies. Put the balls on dinner plates and chill until very firm. You can skip this step if you'd like, but it helps the cookies bake up into neater rounds.
• Space about about one inch apart on ungreased or parchment lined baking sheets. Bake for 15 minutes at 350F. They do not need to be brown, but a little brown around the edges is okay. Let cool directly on the sheets, as they are quite delicate. Once fairly cool, remove to a cooling rack to finish cooling.

Make Icing

• To prepare icing, cream the almost melted butter and powdered sugar with the mixer. If using the lemon zest, add it to the butter and powdered sugar mixture. Beat until it holds together, then add lemon juice one tablespoon at a time just until mixture is spoonable. You can add some more lemon zest to tastes as well.
• Spoon the icing over the cooled cookies allowing it to fall down the sides.