Preheat oven to 350 degrees F. and line an 11 x 7 inch baking dish with parchment paper.
Place butter and sugars into a large mixing bowl or stand mixer. Beat until creamy and well combined. Beat in egg and vanilla mixing well. Add flour, pudding mix, salt, and baking soda, mixing until dough forms. Stir in chocolate chips. Diving dough into two equal parts. Press half of the dough into prepared baking dish. Place cream cheese and sugar into a large mixing bowl. Beat until well combined. Spread over cookie dough layer. Use a cookie scoop to scoop remaining dough over cream cheese layer. Use an offset spatula to press and carefully spread dough over cream cheese layer. Bake for 35-40 minutes, until golden brown on top and set in middle. Remove and let cool completely. When bars are cooled, cut into squares and serve.