In a small bowl, sift together flour, cornstarch and salt and set aside.

In a large mixing bowl, beat butter and powdered sugar until light and fluffy. Mix in vanilla and lime zest.

Gradually mix in the dry ingredients until well blended. Stir in pistachios (reserve a little bit to decorate the cookies if desired.)

Shape the dough in to a flat disk. Wrap in plastic wrap and refrigerate one hour.

Preheat oven to 350º.

On a lightly floured surface, roll out the dough to ¼ inch thick. Cut the dough in to desired shapes. Place the cookies 1 inch apart on ungreased cookie sheets or cookie sheets lined with parchment paper.

Bake until lightly browned on the bottom about 10-12 minutes. Don't over bake. Cool for 5 minutes on the cookie sheet and then remove to a wire rack to cool.

Icing

Whisk together powdered sugar and lime juice to create a thin glaze. Spread the glaze on each cookie and sprinkle with additional finely chopped pistachios.