1In large bowl, beat 1 cup of the granulated sugar, the powdered sugar, butter, oil, milk, vanilla and eggs with electric mixer on medium speed, or mix with spoon. Stir in flour, baking soda, cream of tartar and salt. Cover and refrigerate about 2 hours or until firm.
2Heat oven to 350°F. Shape dough into 1 1/2-inch balls. In small bowl, place remaining 1/2 cup granulated sugar. Coat balls with sugar. On ungreased cookie sheet, place balls about 3 inches apart. Press bottom of drinking glass on each ball until about 1/4 inch thick. If glass starts to stick, press bottom of glass on cookie dough as needed before pressing balls of dough (the fat in the dough helps to grease the bottom of the glass). Sprinkle each cookie with a little additional sugar.
3Bake 12 to 14 minutes or until set and edges just begin to turn brown. Immediately remove from cookie sheet to cooling rack.