Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream together butter and cream cheese until light and fluffy (about 2 minutes).
Add granulated sugar and mix until incorporated.
Scrape down the bowl, then add eggs and vanilla extract. Mix until smooth.
Gradually add flour, powdered sugar, pudding mix, baking soda, and salt. Mix on low speed until a soft dough forms.
Scoop 1 1/2 tablespoons of dough per cookie and roll in granulated sugar.
Place dough balls on the baking sheet, spacing 2 inches apart.
Flatten each dough ball slightly using the bottom of a drinking glass.
Bake for 9-11 minutes, or until cookies are slightly puffed and cracked on top.
Cool on the baking sheet for 10 minutes, then transfer to an airtight container.
Refrigerate for at least 30 minutes before serving for the best cheesecake-like texture.
