In a medium bowl, cream the butter and sugar. Stir in the flour and vanilla. Roll dough into two logs about 10 inches long. Roll dough logs in finely chopped nuts so that the whole surface is coated. Wrap in plastic and refrigerate for up to two hours.
Preheat oven to 350 degrees F (175 degrees C). Slice dough logs into 1/4 inch thick slices and place them on a cookie sheet. Bake in the preheated oven for 7 to 9 minutes.
