Preheat oven to 375°
Melt butter and shortening
Add sugars to the melted butter and shortening, mixing well
Add egg, then beat until it becomes a light-colored mixture
In separate bowl, sift together the flour and baking soda
Stir dry ingredients into shortening mixture
Add in vanilla and nuts
Shape the mixture into rolls, approximately 1-1/2 inches in diameter
Roll in wax paper
Place in refrigerator and chill thoroughly
Cut rolls into thin slices
Bake on ungreased cookie sheet for 10 minutes