Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy, about 2-3 minutes.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the chocolate chips.
Spread the cookie dough evenly into the prepared baking pan. Bake for 25-30 minutes, or until the edges are golden and a toothpick inserted in the center comes out clean.
Allow the cookie cake to cool completely in the pan on a wire rack.
While the cake cools, prepare the cream cheese frosting. In a mixing bowl, beat together the softened cream cheese and butter until smooth. Gradually add the powdered sugar and vanilla extract, mixing until well combined. If the frosting is too thick, add milk one tablespoon at a time until desired consistency is reached.
Once the cookie cake is completely cool, spread the cream cheese frosting evenly over the top.
Cut into squares and serve.