To measure the flour, lightly spoon into a measuring cup, then level with a straight edge such as the dull edge of a knife. Do not scoop the flour because you will end up with too much flour in the cookies. Put flour into a large mixing bowl.
Add the cream of tartar, baking soda, and salt to the flour. Whisk to combine. Set aside.
Into the bowl of a stand mixer, add the butter, vegetable oil, white sugar and powdered sugar. Mix together on medium speed for 1 minute.
Add the eggs, water and vanilla extract to the butter mixture. Mix on medium speed for 1 minute.
Add the flour a cup at a time, mixing lightly after each addition. If using a stand mixer, toggle the speed switch to the "stir" setting a few times after each addition. After the final addition of flour, mix on medium speed for 30 seconds or just until the flour mixture is well blended with the wet mixture. The dough should be soft, but not sticky.
To check for dough consistency, pick up some of the dough from the bowl and roll it in your hands to make a ball. The dough should be quite soft yet easy to handle and should not be sticky. If dough is sticky, blend in a little more flour, 1 tablespoon at a time, testing as previously instructed after each addition.
To form the cookies, gather approximately 3 tablespoonsful of dough together and roll into a ball about the size of a golf ball. I used a 1.5 tablespoon cookie scoop and put two scoops of dough together to make the appropriate size dough ball. Place 8 balls of dough, staggered, on the baking pan.
Put about 1/4 cup white granulated sugar in a small bowl. Set aside. Very lightly grease the bottom of a drinking glass. Dip the bottom of the glass in the sugar. Gently and evenly press a dough ball with the sugared glass bottom just until the dough squishes out about 1/4-inch from the edges of the glass. The edges of the dough will crack; this is what they are supposed to do. Repeat process with the remaining dough balls, dipping the bottom of the glass into the sugar before pressing the next dough ball. (The glass will not have to be greased between cookies.)
Bake for 8-10 minutes. The cookies are supposed to be pale on top with a very light tan bottom. To check the bottom of the cookie, use a cookie spatula to carefully lift and edge of the cookie. Allow the cookies to cool on the pan for about 2 minutes before removing them to a cooling rack. Allow cookies to cool completely before frosting.