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 melted butter and sugar until well combined. Whisk in eggs, sourdough discard, and vanilla extract until the mixture is smooth and homogeneous.
03 - Sift flour, cocoa powder, and salt directly into the wet mixture. Fold gently with a spatula until just incorporated — avoid overmixing to keep the brownies tender. Set aside.
04 - In a separate medium bowl, beat softened cream cheese and sugar together until smooth and creamy. Add egg and vanilla extract, mixing until fully blended and no lumps remain.
05 - Spread approximately three-quarters of the brownie batter evenly across the bottom of the prepared pan. Pour the cheesecake mixture over the brownie base in an even layer. Dollop the remaining brownie batter on top and use a skewer or knife to swirl through the layers, creating a marbled pattern.
06 - Bake for 32 to 36 minutes, or until the center barely jiggles when gently shaken and a toothpick inserted comes out with moist crumbs attached.
07 - Cool completely in the pan on a wire rack. Refrigerate for 1 to 2 hours before cutting into 16 bars for the cleanest edges.