Preheat your oven to 325°F. (163°C) With cooking spray, spray the sides and bottom with cooking spray or line a 8x8 inch baking pan with parchment paper, leaving some overhang for easy removal. You can use metal binder clips to clip each side so the parchment paper does slide around.
In a large microwave safe bowl, melt the unsalted butter and both sugar in 30 second increments until the butter dissolves into the sugars. Whisking after each increment, This will take about 3-4 increments.
Next whisk in the eggs one at a time, whisking after each addition. Add in the vanilla and mix until combined.
With a rubber spatula, fold in the dark cocoa powder, all-purpose flour, and salt into the wet ingredients. Mix until just combined. Be careful not to overmix.
If desired, fold in the chocolate chips into the brownie batter.
Reserve ¼ cup (just eyeball it) for the swirls on the top. Pour the majority of the brownie batter into the prepared baking pan, spreading it evenly with a spatula. Set aside while you make the cheesecake filling.
For The Cheesecake Filling
In a separate mixing bowl, beat the cream cheese until smooth using a hand mixer or stand mixer fitted with the paddle attachment.
With a rubber spatula, scrape down the sides AND bottom of the bowl. With the mixer on medium to low speed, slowly sprinkle in the granulated sugar until its well combined. The mixture should look smooth!
Scrape the sides and the bottom, and on medium speed, add in the egg. Beat until combined and the mixture is smooth and creamy. Be careful to not over mix!
Using the back of a spoon or a small offset spatula, carefully spread the cream cheese mixture over the brownie batter in the baking pan, creating an even layer.
Drop small spoonfuls of the extra brown batters randomly across the top. Using a knife gently swirl the cream cheese mixture into the brownie batter to create a marbled effect. Make sure not to over-swirl, as it can mix the layers too much and blur the distinction between the brownie and cheesecake layers.
Bake in the preheated oven for 35-40 minutes, or until the edges are set and a toothpick inserted into the center comes out with moist crumbs (not wet batter).
Remove the cheesecake brownies from the oven and let them cool completely in the pan on a wire rack for 20 minutes. Then transfer the entire pan to the fridge for at least 2 hours to set up in the fridge.
Once cooled, carefully lift the brownies out of the pan using the parchment paper overhang and transfer them to a cutting board.
Cut the cheesecake brownies into squares or rectangles and serve.