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 large mixing bowl, stir together the melted butter and sugar until well combined. Whisk in the eggs, sourdough discard, and vanilla extract until the mixture is smooth.
03 - Sift the flour, cocoa powder, and salt into the wet mixture. Fold gently until just incorporated — avoid overmixing. Set the brownie batter aside.
04 - In a separate medium bowl, beat the softened cream cheese and sugar together until smooth and creamy. Add the egg and vanilla extract, mixing until fully blended.
05 - Spread about three-quarters of the brownie batter evenly across the bottom of the prepared pan. Pour the cheesecake mixture over the brownie base. Dollop the remaining brownie batter on top in spoonfuls, then use a skewer or knife to swirl through the layers for a marbled effect.
06 - Bake for 32 to 36 minutes, or until the center barely jiggles and a toothpick inserted comes out with moist crumbs clinging to it.
07 - Cool completely in the pan, then refrigerate for 1 to 2 hours before slicing into 16 bars for the cleanest edges.