Preheat the oven: Set oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper, leaving an overhang for easy removal.
Make the brownie batter: In a large bowl, whisk melted butter and sugar until combined. Add eggs and vanilla extract, mixing well. Sift in cocoa powder, flour, and salt, then stir until just combined. Fold in chocolate chips if using. Spread ¾ of the batter evenly into the prepared pan.
Prepare the pumpkin cheesecake layer: In a separate bowl, beat softened cream cheese and sugar until smooth (about 1 minute). Add pumpkin puree, egg, pumpkin pie spice, and vanilla extract, then mix until creamy and lump-free.
Assemble the layers: Pour the pumpkin cheesecake mixture over the brownie batter, spreading evenly. Dollop the remaining brownie batter in small spoonfuls on top. Use a knife or toothpick to swirl the batters together for a marbled effect.
Bake the brownies: Bake for 30-35 minutes, or until the center is set and a toothpick inserted comes out with moist crumbs. Cool in the pan for 20 minutes, then transfer to a wire rack to cool completely.
Slice and serve: Cut into 16 squares. Serve at room temperature or chilled.
