Using an electric hand mixer, beat together the softened butter, vanilla, powdered and granulated sugars in a large mixing bowl on high speed. It takes about 1-2 minutes for the butter to become lightly whipped.
Form the cookie dough into a ball and place it on top of a sheet of parchment paper. Then press it down and put another piece of parchment paper on top. Now roll it out with a rolling pin to about 1/4-1/2 inches thick.