Sift the cornstarch, flour, and salt together in a small bowl.
In a separate bowl, use the electric mixer to cream the butter and 1/2 cup of the confectioners' sugar together. Add the vanilla extract. Gradually add the dry ingredients and continue mixing until the dough comes together in a ball.
Preheat the oven to 375 degrees F.
Knead the dough briefly on a lightly floured surface. Divide the dough into 10 equal portions. Roll each portion into 1/2-inch diameter ropes. Cut each rope into 2 1/2-inch lengths. Gently roll each length so that the tips are tapered. Place the cookies 1 1/2 inches apart on a sheet pan and curve them slightly to resemble crescents. Refrigerate for 1/2 hour before baking to prevent spreading.
Bake for 10 to 12 minutes in the middle rack of the oven. Cool for 3 minutes. Use a spatula to transfer the cookies directly onto a cooling rack. Dust generously with remaining 1 cup of confectioner's sugar. Use the remaining sugar to dust the cookies again just prior to serving.
The cooled cookies can also be dipped in or drizzled with melted semi-sweet chocolate.