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 at 300ºF 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-inches. Cut into 2 x 1-inch strips. Place 1-inch apart on ungreased baking sheets. Prick with a fork. Bake as above.