In the bowl of a stand mixer, combine the butter, granulated sugar, and confectioners' sugar, and mix until just combined.
Drizzle in oil and pour in eggs, water, and vanilla extract and mix well.
In another bowl, whisk together flour, cocoa, salt, baking soda, and cream of tartar.
Slowly add the flour mixture to the butter mixture and allow the mixer to combine until the dough pulls away from the sides of the mixer bowl.
Using an ice cream/cookie scoop, scoop out golf-ball-size portions on a parchment-lined cookie sheet.
Roll out each cookie dough ball until it is smooth and round.
Using a kitchen glass that has been pressed into granulated sugar, press down on each cookie dough ball until the center of the cookie is pressed flatter than the edges. Repeat this on all cookies.
Bake for 8-12 minutes or until edges are just slightly starting to brown and center no longer appears wet. Allow the cookies to cool as you make the frosting.
NOTE: It is important to NOT over-bake the cookies. Be sure to check your cookies at 7 minutes. Every oven is different and overbaking can result in a tough, crumbly, tasteless cookie. Let your first batch be a test batch so you can ensure the remaining cookies are perfect and soft!