Preheat oven to 350° F. Line a baking sheet with either parchment paper or a silicone baking mat.
In the bowl of a stand mixer or with an electric hand mixer, cream together the butter, cream cheese, and granulated sugar until light in color and fluffy in texture.
Scrape the sides of the bowl and then add in the eggs and vanilla. Mix until well combined.
Add the flour, powdered sugar, cheesecake pudding mix powder, baking soda, and salt. Mix until the dough comes together. The dough will be very soft and sticky.
Scoop the cookie dough using a #40 scoop (1 1/2 tbsp of dough) and then roll the dough in granulated sugar before arranging on the prepared cookie sheet.
Once all of the cookie dough has been prepped, use the bottom of a drinking glass the press the cookies flat. The cookies will not spread or flatten at all when baked, they will puff up slightly.
Bake at 350° F for 9-11 minutes. The cookies will puff up and begin to crack when they are supposed to come out of the oven.
Allow the cookies to cool completely on the pan and then chill before serving, if desired. (I like them best chilled!)