Whisk together the flour and cornstarch. Set aside.
Beat butter and powdered sugar together until light and fluffy.
Beat in key lime juice and zest.
Mix in flour mixture just until combined.
Refrigerate dough for at least 1 hour.
Preheat oven to 350F.
Line cookie sheets with parchment paper or spray with cooking spray.
Scoop out cookie dough (about 1.5 tablespoons) and form into a ball.
Place on prepared cookie sheet and bake for 17-19 minutes or just until tops begin to turn golden.
Remove and promptly sift powdered sugar over the top of the cookies. Lots of powdered sugar. Let the cookies cool completely on the cookie sheets. Do not move them until they have cooled.