01 - Preheat the oven to 350°F. 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 completely smooth. Remove from heat and whisk in the sugar until well combined.
03 - Allow the chocolate mixture to cool for 3 to 5 minutes. Whisk in the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the vanilla extract and sourdough starter until evenly blended.
04 - Gently fold in the all-purpose flour and salt using a spatula, mixing until just incorporated. Do not overmix.
05 - Reserve 1/4 cup of the brownie batter for the swirl topping. Pour the remaining batter into the prepared pan and spread it into an even layer.
06 - In a medium bowl, beat the softened cream cheese with the sugar using an electric mixer or whisk until smooth and lump-free. Add the egg and vanilla extract, then beat until creamy and well combined.
07 - Spread the cheesecake mixture evenly over the brownie base in the pan, covering the surface completely.
08 - Drop small spoonfuls of the reserved brownie batter over the cheesecake layer. Use a skewer or butter knife to drag through the dollops, creating decorative swirls across the surface.
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 - Let the bars cool completely in the pan on a wire rack. Then refrigerate for at least 1 hour before lifting out using the parchment overhang and slicing into 16 squares.