Preheat the oven to 350F with a rack placed in the middle position. Coat a 8"x8" baking pan in non-stick spray and line the pan with parchment paper.
Prepare the Brownie Batter
Place the chocolate chip and the butter in medium glass or metal bowl. Create a water bath by placing the bowl over a pot of simmering water. Make sure the water does not touch the bottom of the bowl. Stir with a rubber spatula just until the chocolate has melted. Remove from the heat.
Whisk the cocoa powder and espresso powder into the melted chocolate. Set the chocolate mixer aside and let it cool slightly.
In a large bowl, beat the eggs and granulated sugar together with a hand mixer until light in color. Add the vanilla and salt and mix to combine.
Pour the chocolate mixture into the egg mixture and beat together to combine. Continue by adding the flour and stirring until just combined.
Measure out ⅓ cup of the batter and set aside. Pour the remaining brownie batter into the prepared pan and level it with a spatula.
Prepare the Pumpkin Cheesecake Batter
Take the brick of cream cheese from the refrigerator and place it in a microwave safe bowl. Microwave on high for a minute to soften it.
Add the pumpkin puree to the cream cheese and beat with the hand mixer until smooth. Add the egg, brown sugar, cinnamon, and nutmeg to the cream cheese and mix the batter until smooth again.
Pour the pumpkin cheesecake mixture over the brownie batter in the pan.
Take the reserved ⅓ cup brownie batter and dot it on top of the pumpkin batter with a teaspoon. If the reserved brownie batter has hardened, very gently warm it up before dotting it. Use a toothpick to swirl the brownie dots in the pumpkin cheesecake.
Place the pumpkin cheesecake brownie into the preheated oven. Bake for 30-35 minute. Remove the brownie from the oven and let it cool in the pan completely before removing and cutting it up.