Preheat oven to 350 degrees. In a large bowl, combine both sugars , butter and oil; blend well. Add orange peel vanilla and egg and blend well. Add all dry ingredients and mix well. Stir in cranberries.
Drop by rounded teaspoonfuls 2 inches apart onto ungreased cookie sheets. Bake at 350 degrees for 10-15 minutes or until the bottoms are light golden brown. Cool 1 minute then remove from cookie sheet. Then cool 15 minutes more and coat with powered sugar.