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 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 and glossy.
03 - Sift the 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 the softened cream cheese and sugar together until creamy and lump-free. Add the egg and vanilla extract, mixing until evenly blended.
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 over the cheesecake in scattered spoonfuls. Drag a skewer or knife through the layers in figure-eight motions to create a marbled swirl effect.
06 - Bake for 32 to 36 minutes, or until the center barely jiggles when gently shaken and a toothpick inserted into the center comes out with a few moist crumbs attached.
07 - Cool completely in the pan on a wire rack. Transfer to the refrigerator and chill for 1 to 2 hours for clean, tidy slices. Using the parchment overhang, lift the slab out and cut into 16 even bars.