Preheat oven to 350 with rack in center.
In the bowl of a stand mixer with paddle attachment, cream butter for about 20 seconds. Add 2/3 cup powdered sugar and salt and cream to combine. Add vanilla and combine.
Sprinkle the cornstarch over mixture but do not combine (the corn starch will help disperse the flour evenly).
Add one cup of flour over the corn starch and blend slowly. Add the ½ cup of flour and the half cup of coconut flour and blend to combine.
Remove bowl from mixer and add chopped pecans or walnuts, mixing by hand.
Roll out the dough into a log and cut in half. Cut each half in half. Cut each quarter in half. You now have eight mini logs. Cut each of these into thirds to yield 24 total pieces.
Roll each piece into a ball and place on parchment lined cookie sheets and bake one pan at a time for 18 minutes.
Place one cup of powdered sugar into medium bowl.
Once pan(s) come out of oven, let pan cool for 5 minutes then roll each cookie in the powdered sugar and place on a rack to finish cooling.
Once completely cool, roll again in the powdered sugar and press sugar to thickly coat all sides. Use the other ½ cup of sugar if needed.
Store cookies tightly covered and eat within a few days.