01 - Preheat the 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. Remove from heat and whisk in the sugar until combined.
03 - Let the chocolate mixture cool for 5 minutes, then whisk in the eggs one at a time until fully incorporated. Stir in the vanilla extract and sourdough starter, mixing until smooth.
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 until smooth and creamy. Add the egg and vanilla extract, beating until fully combined and lump-free.
07 - Spread the cheesecake mixture evenly over the brownie base in the pan, covering the surface completely.
08 - Drop spoonfuls of the reserved brownie batter over the cheesecake layer. Use a knife or skewer to drag through the batter, 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 - Allow the bars to cool completely in the pan on a wire rack. Refrigerate for at least 1 hour before cutting into 16 squares.