Cream sugar, butter, powdered sugar, and oil.
Then cream in eggs and vanilla.
In a separate bowl mix baking soda, cream of tartar, and flour.
Start adding dry ingredients to creamed ingredients less than 1 cup at a time.
Chill in refrigerator at least 2 hours.
Drop 1-2" balls on the cookie sheet.
If you would like, you can flatten the balls with the bottom of a drinking glass that has been dipped in sugar.
Bake at 350° for 10-12 minutes or until the edges are browned.
You can also sprinkle on cinnamon and sugar, colored sugar sprinkles, etc.