Smooth out the cream cheese. In a large mixing bowl (if using a stand mixer, use your paddle attachment), mix the cold cream cheese on low speed until creamy and until no lumps remain. Try to mix as little as possible and stop just when it is smooth. You can check with a spatula by smearing it around a little and then scrape out the cream cheese into another small bowl and set aside.

Smooth out the butter. Cut the cold butter into chunks so it’s easier to work with and add to the same bowl (no need to clean the bowl or attachments). Cream until smooth and there are no visible lumps.

Add the powdered sugar in increments. Add about a third of the powdered sugar; you can eyeball this. Start on low speed and gradually mix. Once it's all mixed in, add the next third of powdered sugar and mix. When adding the last third of the sugar, add the vanilla, cream of tartar, and salt. Cream cheese comes already salted, so start with a pinch and correct it by tasting at the end. (If you're using a hand mixer, this is the longest part and may take a few minutes. I like to make a scraping motion while mixing to help everything come together faster.)

At the end of this step, you’ll have a white, very thick sugar-butter mixture that you can pick up with your fingers. It will look and feel like white clay.

Add cream cheese and smooth out the buttercream. Add all the smooth (and still cold) cream cheese to the butter-sugar mixture. Mix on low speed and stop just when all the lumps disappear. You can use a spatula to do the final mixing because it will thin out once the cream cheese has been added. Try to avoid over-mixing at this point; you want to stir the cream cheese into the butter-sugar mixture rather than whip it or mix it at high speed.