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. Remove from heat and whisk in the sugar until well combined.
03 - Allow the chocolate mixture to cool for 5 minutes. Whisk in the eggs one at a time, beating well after each addition. Stir in the vanilla extract and sourdough starter until fully incorporated. Gently fold in the flour and salt until just combined — do not overmix.
04 - Reserve 1/4 cup of the brownie batter and set aside. Pour the remaining batter into the prepared pan and spread into an even layer.
05 - In a medium bowl, beat the softened cream cheese and sugar together until smooth and lump-free. Add the egg and vanilla extract, then beat until creamy and well blended.
06 - Spread the cheesecake mixture evenly over the brownie base in the pan.
07 - Drop small dollops of the reserved brownie batter over the cheesecake layer. Using a knife or skewer, drag through the batter in a figure-eight motion to create decorative swirls.
08 - Bake for 30 to 35 minutes, or until the center is just set and a toothpick inserted comes out with a few moist crumbs. Avoid overbaking for the fudgiest texture.
09 - Let cool completely in the pan on a wire rack. Refrigerate for at least 1 hour before slicing into 16 bars for clean edges.