Preheat your oven to 350°F (175°C) and grease a 9x9-inch baking pan.

In a medium saucepan, melt the unsalted butter over low heat. Remove from heat and stir in the granulated sugar. Mix in the eggs and vanilla extract until well combined.

In a separate bowl, whisk together the cocoa powder, all-purpose flour, salt, and baking powder. Gradually add this dry mixture to the butter mixture, stirring gently until just combined.

In a mixing bowl, beat the softened cream cheese and granulated sugar together until smooth. Add the pumpkin puree, egg, vanilla extract, and pumpkin pie spice, mixing until well combined.

Pour half of the brownie batter into the prepared baking pan. Spoon the pumpkin cheesecake mixture over the brownie layer, spreading it gently. Drop spoonfuls of the remaining brownie batter on top and swirl with a knife.

Bake for 30-35 minutes, checking for doneness with a toothpick. It should come out with a few moist crumbs.

Let the brownies cool in the pan for at least 15 minutes before slicing into squares.