In a small bowl, combine potato starch, flour and salt.
Beat butter, vanilla and sugar until creamy.
Add flour mix a little at a time, until you have a homogenous cookie dough.
Wrap in plastic wrap and refrigerate for 2 hours.
Roll out dough on a well floured surface to about 1/2" thick. You don't even need a rolling pin. You can just pat it down using the palm of your hand. It's a very soft dough. Using cookie cutters, dip them in flour and then cut out cookies and place on parchment lined cookie sheet.
Bake for 15 minutes.
Notes
If you have a Kitchen Aid, you can beat the butter and sugar when the butter is cold right out of the refrigerator, using the paddle attachment. You will then only need to refrigerate the dough for 1/2 hour.