Preheat your oven to 350°F (175°C) and grease a 9x9 inch baking pan.
In a medium mixing bowl, whisk together the flour, cocoa powder, baking powder, and salt.
In a larger bowl, blend the melted butter and granulated sugar until creamy. Add the eggs one at a time, then stir in the vanilla extract.
Gradually add the dry mixture to the wet mixture, stirring gently. Pour half of the brownie batter into the prepared pan.
In a separate bowl, beat the cream cheese with powdered sugar until smooth. Incorporate the additional egg, then add the pumpkin puree, cinnamon, and nutmeg, mixing until uniform.
Spoon the pumpkin cheesecake mixture over the brownie batter in the pan.
Dollop the remaining brownie batter over the pumpkin layer and swirl with a knife or toothpick.
Bake for 30-35 minutes, checking for doneness with a toothpick.
Let the brownies cool in the pan for 10-15 minutes before transferring to a wire rack to cool completely.
Notes
Serve on a decorative platter, dusted lightly with powdered sugar and topped with whipped cream.