Cream the butter and add the sugar and vanilla and beat to fluffy. Add the flour and nuts and mix in. Chill the dough for at least one hour. The more it's chilled the less it spreads during baking.
Preheat oven to 350 degrees F.
Shape the dough into tiny crescents using 1 teaspoon of dough for each cookie. Place them on an ungreased sheet pan in rows, leaving 1 inch in between for spreading and bake until golden brown, about 12 to 15 minutes.
Let cool 5 minutes. Dredge them in confectioners' sugar.