In a mixing bowl, beat butter with electric mixer on medium to high speed for 30 seconds. Add 2/3 cups xylitol and baking soda. Beat until combined while scraping sides of bowl. Beat in egg and vanilla until combined then beat in flour.
Spoon mixture onto cookie sheet (about a tablespoon size balls). Combine left over xylitol and cinnamon and sprinkle on each cookie. Bake at 375®F for about 10 minutes or until they begin to turn brown.