In a mixing bowl, cream your butter, and sugars. Once white and creamy in texture, add flour, cornstarch, vanilla, and salt. Mix until it starts to stick together. Roll the dough into balls and wrap in plastic. Chill for 30 minutes.
Preheat oven to 325°F.
Roll your dough out onto a lightly powdered sugar surface. Roll and cut into shapes. Place shapes on a greased cookie sheet. Bake cookies for 8-10 minutes, or until the cookies are set. Allow to cool on a wire rack.
Make your frosting by combining the above ingredients. Add enough milk so that your frosting can drizzle but is not too runny. Glaze your cookies and allow the icing to set before serving. Serve and enjoy!
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