01 - Preheat oven to 350°F. Line an 8×8-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.
03 - Remove the saucepan from heat and stir in the granulated sugar until fully dissolved into the chocolate mixture.
04 - Allow the mixture to cool slightly, then whisk in the eggs one at a time until well blended. Stir in the vanilla extract and sourdough starter, mixing until smooth and combined.
05 - Gently fold in the all-purpose flour and salt until just incorporated — do not overmix. Reserve 1/4 cup of batter for the swirl topping.
06 - Pour the remaining brownie batter into the prepared pan and spread it into an even layer across the bottom.
07 - In a medium bowl, beat the softened cream cheese with granulated sugar using an electric mixer or whisk until smooth and lump-free. Add the egg and vanilla extract, beating until creamy.
08 - Spread the cheesecake mixture evenly over the brownie batter in the pan, covering the surface completely.
09 - Dollop spoonfuls of the reserved brownie batter over the cheesecake layer. Use a skewer or knife to drag through the dollops, creating decorative swirls.
10 - Bake for 30–35 minutes, or until the center is just set and a toothpick inserted comes out with a few moist crumbs attached.
11 - Let the bars cool completely in the pan on a wire rack. Refrigerate for at least 1 hour before slicing into 16 squares.