Beat butter until nice and fluffy, continue to beat (lowering speed) and add in sugars.
Stop mixer and scrape the sides of the bowl. Add eggs, 1 at a time, followed by vanilla and almond extract, then oil. Add baking soda, cream of tartar and salt.
Add flour 1 cup at a time, mixing thoroughly.
Roll dough into walnut-sized balls (or drop onto baking sheets using a cookie scoop 2-Tbsp.) and bake on an ungreased cookie sheet for 12 minutes.
Cool cookies 3-5 minutes on the pan then transfer to a rack.
Beat butter with an electric mixer on high speed until fluffy. Add powdered sugar, cocoa, vanilla, and milk*. Beat on low speed until ingredients come together then mix on high speed for 3 minutes, occasionally scraping the side of the bowl with a rubber spatula, until fluffy. *If more milk is needed, add it 1 teaspoon at a time.
Fit a piping bag or large plastic storage bag with a 2D frosting tip.
Frost-cooled cookies with chocolate rosettes. (Watch my video to see how I do this)Add sprinkles, if desired.
Video
Notes
Store cookies in an airtight container.The frosting will set up slightly as the cookies stand, enough to stack 2 cookies tall after a few hours.Cookies can be stored at room temperature or chilled.Optional: use 1 teaspoon of vanilla extract and 1 teaspoon of cake batter flavoring.