Before getting started, preheat your oven to 350ºF, and line a large cookie sheet with parchment paper.
In a large bowl or in the bowl of an electric stand mixer, cream together the butter, cane sugar, powdered sugar, egg, and vanilla extract.
In a separate bowl, whisk together the flour, baking soda, cream of tartar, baking powder, and salt.
Add the flour mixture to the butter mixture, mixing 'til well combined.
Scoop the dough into balls and place on a cookie sheet.
Bake at 350° F for 8-10 minutes, or 'til the cookies start to turn a slight golden color.
Using a cookie spatula, remove the cookies to a wire rack to cool.