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 lemon zest. Gradually mix in the dry ingredients until well blended. Shape the dough in to a flat disk. Wrap in plastic wrap and refrigerate one hour.
Preheat oven to 350°
On a lightly floured surface, roll out the dough to ⅛ inch thick. Cut the dough in to an egg shape. On half of the cookies, use a tiny chick cookie cutter to cut out a chick in the center of the egg. Gather up the scraps and roll out the dough again to create as many cookies as possible.
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 8-10 minutes. Don't over bake. Cool for 5 minutes on the cookie sheet and then remove to a wire rack to cool.
When cookies are cool, spread the lemon curd on the bottoms of the solid cookies and top with a chick cookie. Dust the tops with powdered sugar.