Preheat the oven to 350°F. Grease a 9x9-inch baking pan and line with parchment paper, then set aside.
In a mixing bowl, put together ½ cup chocolate chips (or a chopped chocolate bar) and ½ cup cubed butter. Melt in 30 second increments in the microwave, stirring in between.
When done, mix it well and add 1 cup granulated sugar. You want to whisk it very well, so the sugar dissolves. Then add 2 eggs and 1 tsp vanilla extract and whisk again.
Add ¾ cup all-purpose flour and sift ¼ cup coco powder, fold it in.
Scoop out about ¼ cup of the mixture in a separate small bowl and set aside.
In another mixing bowl, using a hand mixer, beat together 8 oz cream cheese and ¼ cup sugar, until light and fluffy. Add an egg and 1 tsp vanilla extract and beat again.
Pour the brownie layer in a pre-greased baking pan, and using a spatula, spread evenly, trying to keep the same thickness on all sides.
Pour the cheesecake layer on top and spread it evenly as well.
In a small bowl with the remaining brownie mixture, pour 1 tablespoon of water and mix very well until smooth.
Dollop the brownie batter over the cheesecake layer. Using a toothpick or a tip of a knife, make the swirls. (You can watch the video tutorial for visual details).
Bake at 350°F for about 30 minutes.
When done, take it out of the oven and let cool completely, then cut in 12 squares.