Cream together butter, canola oil, sugars, water, eggs, baking soda, cream of tartar and salt in a large mixing bowl with electric mixer.
Add flour and stir with a wooden spoon until thoroughly mixed.
Roll dough into golf ball-sized balls and place three inches apart on greased cookie sheets.
Combine ¼ cup granulated sugar and a pinch of salt in a small bowl.
Dip the bottom of a flat drinking glass into the sugar mixture.
Firmly press each dough ball with the sugar-coated glass.
Bake cookies at 350° for 12-15 minutes or until lightly browned on the bottom.
Rotate cookie sheets on oven racks after seven minutes of baking time.
Remove to cookie rack.
Refrigerate cookies once cool. (I omitted this step).
Add icing and allow to set up.
Refrigerate cookies until ready to serve.