Adjust oven racks to middle position and preheat oven to 350 °F (177 °C). Line a 9x9" baking pan with parchment paper and leave a one-inch over-hang on either side. Spray with non-stick baking spray and set aside.
Whisk cocoa, espresso, and boiling water in a large bowl until smooth. Add unsweetened chocolate and whisk until melted. Whisk in butter and vegetable oil. The mixture might look a little funky, but it's ok. Add eggs, egg yolks, and vanilla extract and continue to whisk until mixture is smooth and everything is combined.
Whisk in sugar until fully incorporated then whisk in flour and salt. Fold in the bittersweet chocolate pieces.
Pour batter into prepared baking pan and set aside while you make the pumpkin cheesecake topping.
In the bowl of a stand mixer, beat together cream cheese and sugar until light and fluffy. Add the pumpkin puree, egg, and pumpkin pie spice. Beat until mixture is smooth and incorporated.
Taking a tablespoon, drop spoonfuls of pumpkin cream cheese batter onto the top of the brownie batter in no particular pattern. Take a toothpick or knife and drag it throughout the batter, swirling the pumpkin and brownie batters together.
Bake the brownies for 35-40 minutes, or until the edges are set and the center is still jiggly. You don't want to over-bake these otherwise they'll be cakey!
Let the brownies cool in the pan for 20 minutes then lift the brownies out of the pan with the parchment paper, and place onto a wire rack to cool completely.
Prior to cutting, place brownies into refrigerator for 30 minutes then use a sharp knife to cut them into squares. Clean off the knife every now and then if it gets too gummy.