In lg bowl, beat butter and oil w/ mixer on medium for 30 seconds. Add 1/2 cup sugar, powdered sugar, baking soda, cream of tartar and salt. Mix well. Beat in egg and vanilla. Slowly beat in flour until mixed well. Wrap w/ plastic wrap and refrigerate for 24 hrs. The next day, heat oven to 375. Place parchment paper on baking sheets. Shape dough into balls, place 2" apart on paper. Flatten balls w/ bottom of a floured glass. Sprinkle w/ colored sugar or sprinkles. Bake 8-12 min, or until bottoms are lightly browned. Transfer to racks and cool. You can also forego the sprinkle and frost the cookies instead.