Preheat oven to 350 °F. Beat butter until light and fluffy. Add the sifted icing sugar and beat again until fluffy, scraping down sides of the bowl often. Add the cornstarch or rice flour and blend in. Add in the all purpose flour and salt and mix until dough comes together (it will be soft). Stir in vanilla. Spoon large teaspoonfuls of cookie dough onto an un-greased cookie sheet, leaving 2 inches between cookies and bake for 18 to 20 minutes, until bottoms brown lightly. Remove from cookie sheet to cool.