Preheat oven to 350 F. Line cookie sheets with parchment paper.
Beat butter, brown sugar and vanilla until light and fluffy. Add flour and cornstarch. Mix until dough forms.
Roll into 3/4" balls. Place on prepared cookie sheets. Flatten slightly. Bake for 10 minutes. Remove and place on wire racks. With a wooden skewer or toothpick, poke 4 holes in warm cookies to make button holes.