Preheat the oven to 350F. With an electric mixer, beat the butter for a good minute or two, until light and pale. Add the icing sugar and vanilla and beat for another minute.
Add the flour, cornstarch and salt; beat just until you have a soft, smooth dough. Roll into 1-inch balls and place on an ungreased cookie sheet. Press each down with a fork, the bowl of a spoon or a cookie stamp. Bake for 12-14 minutes, until set and pale golden on the bottom. Makes about 2 dozen cookies.
Serving Size Makes about 2 dozen cookies.