Butter Cookies: Cream together the butter and sugar until light and fluffy, about
3 minutes, scraping the bowl down as needed. Add the egg yolk, then the vanilla
extract and 1 1/2 teaspoons Key lime juice. Blend in the flour.
Transfer the dough to a large piece of plastic wrap and form into a cylinder
that is 2 1/4 inches in diameter.
Refrigerate for 2 hours or overnight.
Heat the oven to 350 degrees F. Butter 2 large baking sheets and set aside.
Cut the cookies into 1/4-inch slices. Place the slices on the baking sheets and
bake at 350 degrees F for 8 to 10 minutes.
Place the baking sheets onto a cooling
rack and cool for 5 minutes.
Transfer the cookies to the cooling rack.
Key Lime Icing: Combine the confectioners' sugar and 1 1/2 tablespoons Key
lime juice in a small bowl. Brush the tops of the cookies with the icing as soon
as the cookies are transferred off the baking sheets.