Preheat oven to 300°F. 

Mix butter, sugar and vanilla thoroughly using an electric mixer.  Gradually blend in flour and corn starch.

Form into 1-inch balls and place on ungreased baking sheets.  Gently press down on each cookie to flatten using fingers or a flat-bottomed drinking glass (dipped in sugar to prevent sticking).

Bake for 25 to 30 minutes, or until bottoms begin to brown.  Cool for 5 minutes; remove to a wire rack to cool completely.

Recipe Note:  For European-style shortbread, turn dough onto a lightly floured surface and knead until smooth, about 2 minutes.  Pat into a 1/3-inch thick rectangle measuring 11 X 8-inch.  Cut into 2 X 1-inch strips.  Place 1-inch apart on ungreased baking sheets.  Prick with a fork.  Bake as above.