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) and bake on an ungreased cookie sheet for 12 minutes.
Cool 1 minute on pan and transfer to a rack. Store in an airtight container.
Frosting
Mix butter and powdered sugar together using an electric mixer until fluffy.
Stir in vanilla, milk, and marshmallow creme and mix well.
Spread or pipe over cookies.
Video
Notes
Note: if you are going to pipe frosting over the cookies, make a full batch of frosting. If you'd prefer to spread a thin amount over each cookie using a butter knife, you can make half batch of frosting.