Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan and line it with parchment paper for easy removal.
In a large mixing bowl, combine the melted butter and sugar. Stir until well mixed, then add the eggs one at a time, incorporating them fully before adding the next. Mix in the vanilla extract.
In another bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually fold the dry ingredients into the wet mixture until just combined.
In a separate bowl, beat the softened cream cheese until smooth. Add the granulated sugar and mix until well incorporated. Then add the pumpkin puree, egg, pumpkin spice, and vanilla extract; mix until completely smooth.
Pour about two-thirds of the brownie batter into the prepared baking pan, smoothing it out evenly. Next, drop spoonfuls of the pumpkin cheesecake mixture over the brownie base. Finally, dollop the remaining brownie batter on top.
Using a butter knife or a skewer, gently swirl the pumpkin cheesecake mixture into the brownie batter for a marbled effect. Be careful not to overmix.
Place in the preheated oven and bake for 30-35 minutes, or until the edges are set and a toothpick inserted in the center comes out with fudgy crumbs.
Allow the brownies to cool completely in the pan before lifting them out using the parchment paper. Cut into squares and serve.
Notes
Allow brownies to cool completely for best texture before cutting.