Preheat your oven to 350°F (175°C) and grease a 9x9 inch baking dish, or line it with parchment paper for easier removal.
In a medium saucepan, melt the butter over low heat. Once melted, remove from heat and stir in the granulated sugar, eggs, and vanilla extract until well combined.
In a separate bowl, whisk together the cocoa powder, flour, salt, and baking powder.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Pour half of this brownie batter into the prepared baking dish and spread evenly.
In a mixing bowl, beat the softened cream cheese until smooth. Add the pumpkin puree, powdered sugar, pumpkin pie spice, egg, and vanilla extract. Mix until everything is well combined and creamy.
Dollop the pumpkin cheesecake mixture over the brownie batter in the baking dish. Using a knife or a toothpick, gently swirl the cheesecake mixture into the brownie layer for a marbled effect.
Pour the remaining brownie batter on top of the cheesecake layer, and spread it evenly.
Place the baking dish in the preheated oven and bake for 30-35 minutes or until a toothpick inserted into the center comes out with a few moist crumbs (not wet batter).
Once baked, remove from the oven and allow to cool in the pan for at least 20 minutes. Then transfer to a wire rack to cool completely before cutting into squares.
Notes
Allow to cool completely before cutting for clean squares.