Step 1: Preheat your oven to 350°F (175°C) and line an 8×8 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: In a large bowl, whisk together the melted butter, granulated sugar, brown sugar, and 1/3 cup maple syrup until well combined and smooth.
Step 3: Add two eggs and vanilla extract to the brownie mixture, beating well until the batter looks shiny and slightly thickened.
Step 4: Sift in the cocoa powder, flour, and salt. Fold gently with a spatula until no streaks of flour remain. Reserve 1/2 cup of this batter for later.
Step 5: Spread the remaining brownie batter into the prepared pan, smoothing the top with a spatula.
Step 6: In a separate medium bowl, beat the softened cream cheese until smooth. Add the pumpkin puree, 1/4 cup maple syrup, one egg, and pumpkin pie spice. Mix until completely creamy.
Step 7: Pour the pumpkin cheesecake mixture over the brownie layer in the pan.
Step 8: Dollop the reserved 1/2 cup of brownie batter over the pumpkin layer. Use a knife to swirl the batters together in a marble pattern.
Step 9: Bake for 35-40 minutes, or until the edges are set and a toothpick inserted into the center comes out with just a few moist crumbs. Do not overbake.
Step 10: Allow the maple pumpkin cheesecake brownies to cool completely in the pan before lifting them out using the parchment paper and slicing into squares.