Preheat oven to 350°F (175°C). Grease and flour a 9×9 inch baking pan.
In a heatproof bowl set over a saucepan of simmering water (or in the microwave), melt the butter and chocolate, stirring until smooth. Remove from heat and let cool slightly.
Stir in the sugar, then beat in the eggs one at a time, followed by the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
Pour the brownie batter into the prepared baking pan.
In a medium bowl, beat the cream cheese and sugar until smooth and creamy. Beat in the egg, then stir in the pumpkin puree and pumpkin pie spice.
Spoon the cheesecake mixture over the brownie batter. Use a knife or skewer to swirl the cheesecake into the brownie batter.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out with moist crumbs.
Let the brownies cool completely in the pan before cutting into squares.
