Have all ingredients at room temperature (except the boiling water). Preheat an oven to 350F and place the rack in the centre of the oven. Butter a 9x13 baking pan and line with parchment paper. Butter the parchment.
In the bowl of a stand mixer fitted with a paddle attachment, combine cream cheese and maple syrup. Beat on high until creamy with no lumps, stopping the mixer from time to time to scrape down the sides. About 2 minutes.
Add 3 Tablespoons of pumpkin puree, 1 teaspoon vanilla,1/4 teaspoon spice blend and a pinch of salt. Beat well to combine into a smooth mixture. Separate one egg, discarding the white or reserving for another use, and add the yolk to the cream cheese mixture. Crack in one more egg. To be very clear, you are adding 1 whole egg and 1 yolk to the mixer bowl. Mix on medium until just combined. Scrape down the sides, then place the bowl in the refrigerator to chill while you prepare the remainder of the recipe.
Add the bean flour to a medium mixing bowl. Sift in the cocoa powder, baking powder, baking soda, remaining salt and 1 teaspoon pumpkin spice blend. Whisk to combine, then set aside.
In another medium mixing bowl, whisk together the remaining egg with the oil. Add the sugar and beat for 1 minute. Add remaining 1/2 cup pumpkin puree and vanilla; mix to combine.
In a microwaveable bowl or measuring cup, melt butter on HIGH for 25-30 seconds or until melted and very hot. Scrape chopped chocolate into the butter and stir gently with a spatula until the chocolate is melted.
Add the melted chocolate to the bowl with the sugar mixture and fold gently with a spatula to combine. Tip in all of the flour mixture and fold together. Splash in the buttermilk and mix to combine. Lastly, pour in the boiling water and mix until smooth.
Immediately, spread about 2/3 of the brownie batter around the prepared baking pan. Grab the cheesecake mixture from the refrigerator and pour it all over the brownie batter. Dot with remaining brownie batter, then quickly run a toothpick or the blade of a knife through the whole pan to swirl the two batters together.
Place the pan on the centre rack and bake for 27-30 minutes or until the centre of the brownies only *slightly* jiggles when you shake the pan. Try to rotate the pan 180 degrees once halfway through the baking.
Cool brownie pan completely on a wire rack, then transfer to the refrigerator to chill before cutting. To cut, remove the chilled brownies from the pan by lifting the parchment paper. Run a chef's knife under hot running water to warm it, and then make quick, firm cuts into the brownies.
Store brownies in an airtight container, refrigerated for up to 5 days. To freeze: wrap the pan well in plastic and freeze for up to 3 months.
