Make sure your butter and cream cheese have some time to come to room temperature before you start this recipe.
Add the carrot cake mix, vegetable oil, and eggs to a large mixing bowl. Using an electric hand mixer, mix until smooth.
Chill dough for 30 minutes in the fridge (or 15-20 in the freezer). I recommend this step since the dough is sticky and you will also get slightly puffier cookies with chilling.
Meanwhile, preheat your oven to 350F. Line a baking sheet with parchment paper or a Silpat non-stick mat.
Make 2" balls and place them on the baking sheet at least 2" apart, if not more since they do spread. Bake for 11-13 minutes until they're set.
Meanwhile, make the frosting. Add the cream cheese, butter, and vanilla extract to a medium mixing bowl. Mix using an electric mixer, and gradually add the sugar (about 1/2 cup or so at a time) until the frosting is smooth.
Let the cookies cool for a few minutes on the baking sheet, then transfer them to a cooling rack. Give it at least 10 minutes or until they're cool to the touch before you frost them. I sprinkled on some cinnamon sugar for the photos. This step is optional.
Store cookies in an airtight container.