In the bowl of a stand mixer, combine butter, granulated sugar, confectioners' sugar and mix until just combined.
Drizzle in oil and pour in eggs, orange juice, orange zest, and orange extract, and mix well.
In a bowl add the cream of tartar and salt to the flour and roughly sift.
Slowly add the flour 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 7-9 minutes or until edges are just slightly starting to brown and center no longer appears wet. Let the cookies cool while you prepare 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!