Using a mixer, cream together butter and sugar until fluffy, then add vanilla.
In another bowl, sift flours together, then add to wet mixture. Mix until combined.
Turn dough out onto a piece of plastic wrap and shape into a log. Cover and chill for at least an hour. Then slice cookies and place on a baking sheet with parchment paper (cookies won't spread, so can place close together).
Bake at 350°F for 12 minutes.
Notes
For chocolate lovers, dip half the cookie in melted chocolate.