Step 1: Preheat your oven to 350°F (175°C) and grease an 8x8 inch square baking pan or line it with parchment paper.
Step 2: In a large bowl, whisk together the melted butter and sugar until well combined. Add the eggs and vanilla, beating until smooth.
Step 3: Sift in the cocoa powder, flour, and salt. Gently fold the dry ingredients into the wet mixture until just combined. Set aside about 1/2 cup of this batter.
Step 4: In a medium bowl, beat the softened cream cheese until smooth. Add the pumpkin puree, maple syrup, pumpkin pie spice, and egg yolk, mixing until fully incorporated and silky.
Step 5: Spread the main portion of the brownie batter into the prepared pan. Spoon the pumpkin cheesecake mixture over the top in large dollops.
Step 6: Drop the reserved 1/2 cup of brownie batter over the pumpkin layer. Use a knife to swirl the mixtures together gently.
Step 7: 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.
Step 8: Allow the maple pumpkin cheesecake brownies to cool completely in the pan before slicing into 16 squares.