Preheat oven to 350 degrees.
In a separate mixing bowl, mix flour, salt, baking soda and cream of tartar. Set aside.
In a large bowl, cream together butter, sugar and powdered sugar until well blended.
Slowly pour in oil while mixing all the time.
Add water, almond extract and eggs, blending well.
Add dry flour mixture to the wet ingredients and mix until well incorporated.
Roll cookie dough into 2 inch balls.
Put the additional 1/2 cup sugar into a small bowl.
Place the 2 inch balls onto an ungreased cookie sheet about 3 inches apart because they will spread.
Place a glass into the sugar (you may need to press the glass against some cookie dough to get the sugar to start to stick) and then press into the balls of dough.
Press until cookies are about 1/2 inch thick. The edge will become jagged and the cookie will spread beyond the bottom of the glass.
Bake for only 8 minutes. You do not want to over bake these cookies. 8 minutes is just about perfect.
Remove cookies from cookie sheet and transfer to a wire rack to cool.
If you aren't going to frost these cookies right away, place them in an airtight container until ready to frost. This is what keeps them moist. I usually layer them in a gallon size ziploc bag.