Preheat oven to 350°F and line a 9 x 9 pan with parchment paper on all sides. Set aside.
Make the cheesecake layer first. In a stand mixer fit with the paddle attachment beat all the cheesecake ingredients together until combined, about 2 minutes. Do not over beat. Set aside.
Now make the brownie layer. In a microwave-safe bowl, melt the butter. Remove from microwave, stir in sugar. Microwave the mixture for 30 more seconds. Stir again and melt for 60 seconds more. You want the sugar and butter to bubble up slightly, but not burn. This amount of time should do the trick.
Remove mixture from the microwave and stir the bittersweet chocolate into the hot mixture to melt it completely. If the chocolate doesn’t melt completely, put it in the microwave for another 15 seconds.
Add eggs and egg yolk and the vanilla extract, beating until combined. Add the flour, cocoa powder and salt and mix until combined.
Remove a 1/2 cup of the brownie batter and place it in a separate bowl. Add two tablespoons of water to the 1/2 cup of batter and whisk together to thin it out. This will create the brownie swirl on top.
Pour the remaining brownie batter into the prepared pan, spreading it into an even layer. Pour the cheesecake batter over the brownie layer. Drop the remaining thinned out brownie batter onto the cheesecake and use a knife to create a few big swirls. Do not over swirl. You want big separate swirls of cheesecake and brownie.
Bake for 30 minutes, or until a knife inserted into the center of the brownies comes out mostly clean. Allow to cool completely and place in the fridge for an hour for the cheesecake to set. When ready to serve, cut into 9 large squares or 16 smaller brownies!
Don’t feel like making homemade brownies? Or have a mix on hand you’re looking to use up? You can always make a brownie mix instead of homemade brownies for the base of these cheesecake brownies!