In a medium size bowl, cream together the butter, sugar, and vanilla extract.
Stir in the flour until a crumbly dough forms. Press together. Cover or wrap in wax paper or plastic wrap and chill in the refrigerator for at least 30 minutes and up to overnight.
On a lightly floured surface, roll the dough out until 1/4 inch thick or even a little thinner. The dough may be crumbly so you may need to press together as you work and roll slowly. Use a cookie cutter to cut out 15-18 cookies.
Bake at 350°F for 10-12 minutes, until the edges begin to brown. Remove to a cooling rack and allow to cool before eating or storing.