Preheat the oven to 350°F (175°C). Grease and line a 9x9 inch baking pan with parchment paper, leaving a slight overhang for easy removal.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until smooth. Add in the eggs and vanilla extract, mixing until well combined.
Gradually add the flour, baking soda, and salt to the wet mixture. Stir until just combined, then fold in the chocolate chips. Press half of this cookie dough into the bottom of the prepared baking pan.
In another mixing bowl, beat the softened cream cheese until smooth. Add the sugar and vanilla extract, then mix in the eggs one at a time until fully incorporated. Pour the cheesecake mixture over the cookie layer in the baking pan.
Spread the remaining cookie dough on top of the cheesecake layer in clumps.
Melt the butter in a saucepan for the brownie layer. Remove from heat and stir in the sugar, then add the eggs one at a time, followed by the vanilla extract.
In a separate bowl, combine the flour, cocoa powder, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, stirring until just combined.
Pour the brownie batter over the cookie-cheesecake layers in the baking pan. Spread evenly.
Bake in the preheated oven for 35-40 minutes, or until the top is set and a toothpick inserted into the center comes out with a few moist crumbs.
Allow the pan to cool completely, then refrigerate for at least 2 hours before lifting out and cutting into bars.