Beat butter, brown sugar and vanilla thoroughly using electric mixer. Gradually blend in flour and cornstarch. Add chips.
Form into 1-inch balls and place on ungreased baking sheets. Pour sugar on a small plate; dip bottom of drinking glass into sugar and press down on each cookie to flatten. Press center of each cookie with tip of a teaspoon.
Bake in preheated 300 degree F oven for 25 to 30 minutes, or till bottoms begin to brown.
Cool for 5 minutes; remove to a wire rack to cool completely.