Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish and line it with parchment paper, allowing some overhang for easy removal.
In a large bowl, whisk together the melted butter and granulated sugar until combined.
Add in the eggs, one at a time, followed by the vanilla extract, and mix until smooth.
In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, stirring until just combined. Do not overmix.
In another bowl, mix the pumpkin puree, cream cheese, powdered sugar, and pumpkin pie spice until smooth.
Pour half of the brownie batter into the prepared baking dish, spreading it evenly.
Dollop spoonfuls of the pumpkin mixture over the brownie layer and use a knife to swirl it gently for a marbled effect.
Pour the remaining brownie batter on top of the pumpkin mixture and smooth it out carefully.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs (not wet batter).
Allow the brownies to cool completely in the pan before lifting them out using the parchment overhang. Cut into squares and serve.
Notes
Allow brownies to cool completely before cutting for best results.