01 - Preheat the oven to 350°F (175°C). Line an 8 x 8 inch baking pan with parchment paper, leaving an overhang on two sides for easy removal.
02 - In a medium saucepan over low heat, melt the butter and dark chocolate together, stirring constantly until smooth. Remove from heat and stir in the sugar until well combined.
03 - Allow the chocolate mixture to cool slightly, then whisk in the eggs one at a time until fully incorporated. Add the vanilla extract and sourdough starter, mixing until smooth and combined.
04 - Gently fold in the all-purpose flour and salt until just incorporated. Be careful not to overmix.
05 - Reserve 1/4 cup of the brownie batter for the swirl topping. Pour and spread the remaining batter evenly into the prepared baking pan.
06 - In a medium bowl, beat the softened cream cheese with the sugar using an electric mixer or whisk until smooth and creamy. Add the egg and vanilla extract, beating until fully combined and no lumps remain.
07 - Gently spread the cheesecake mixture in an even layer over the brownie batter in the pan, covering the surface completely.
08 - Dollop small spoonfuls of the reserved brownie batter evenly over the cheesecake layer. Use a skewer or knife to gently drag through the batter, creating decorative swirls.
09 - Bake for 30 to 35 minutes, or until the center is just set and a toothpick inserted into the middle comes out with a few moist crumbs attached.
10 - Allow to cool completely in the pan at room temperature. Then refrigerate for at least 1 hour before slicing into 16 even bars.