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 chocolate together, stirring constantly until completely 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 flour and salt until just incorporated — do not overmix.
05 - Reserve 1/4 cup of the brownie batter for the swirl topping. Spread the remaining batter evenly across the bottom of the prepared pan.
06 - In a medium bowl, beat the softened cream cheese with the sugar until smooth and lump-free. Add the egg and vanilla extract, beating until creamy and well combined.
07 - Gently spread the cheesecake mixture in an even layer over the brownie batter in the pan.
08 - Dollop the reserved brownie batter in spoonfuls over the cheesecake layer. Use a skewer or knife to drag through the dollops, creating decorative swirls.
09 - Bake for 30 to 35 minutes, or until the center is just set and a toothpick inserted comes out with a few moist crumbs attached.
10 - Let cool completely in the pan, then refrigerate for at least 1 hour before slicing into 16 bars.