Gather all your equipment and ingredients and preheat your oven to 350℉/180℃; grease a 9x9 inch square baking dish then sprinkle it with the tablespoon of granulated sugar
Start by making the cheesecake layer; in a medium bowl, combine the pumpkin puree and cream cheese and beat with a hand mixer or whisk until smooth
Add the flour, sugar, pumpkin pie spice and vanilla extract and mix again until smooth
Set aside while you make the brownie layer (the brownie layer will thicken as it sits so making it second helps ensure it stays in place when spreading the second brownie layer)
Next, make the brownie layer: in a medium bowl, combine the flour, salt, cocoa powder and espresso powder and whisk until combined and no lumps of cocoa powder remain then set aside
In a heatproof bowl, melt the butter and chocolate together in 15 seconds bursts, stirring once or twice throughout then mix until smooth; set aside to allow to cool slightly
In a large bowl, combine the sugar, vanilla extract, eggs and chocolate mixture and whisk until smooth
Add the dry ingredients to the wet ingredients and mix until just combined, but do not overmix (stop mixing as soon as you can no longer see any flour)
Pour half the brownie batter into the prepared baking dish and spread evenly
Add the pumpkin cheesecake batter over the brownie layer and spread evenly
Dollop the remaining brownie batter over the cheesecake layer and spread evenly (both batters should be thick enough that spreading is fairly easy; if not, either chill cheesecake layer for 5-10 minutes or let brownie batter stand)
Bake for 40-45 minutes or until a toothpick comes out clean with no more than a few crumbs (see Note 5)
Allow to cool completely before cutting into squares