Preheat oven to 350° F. Line an 8 by 8-inch square baking pan with parchment paper and lightly grease with nonstick cooking spray. Set aside.
In a makeshift double boiler over low heat, melt chocolate and butter, stirring occasionally. Remove pan from the heat and whisk in the cocoa. Set aside to cool slightly.
In the bowl of a stand mixer, beat together eggs and sugar on medium-high speed for 1 minute. Reduce speed to low and add vanilla and salt until combined, about 15 seconds. Keep mixer on low and slowly pour in chocolate mixture into the egg mixture (you can also stir it in by hand).
Remove bowl from mixer and stir in the flour with a wooden spoon until just combined.
Set aside ¼ cup batter. Pour remaining batter in prepared baking pan. Spread evenly.
For the topping, use an electric mixer to beat cream cheese until smooth and creamy. Add pumpkin puree, egg, sugar and vanilla. Mix until combined. Scrape down the sides and bottom of the bowl as necessary.
Drop dollops of cream cheese mixture onto prepared brownie batter. Spread into an even layer. If the reserved batter became stiff, give it a good stir, then drop spoonfuls of the batter on top. Use a knife to swirl the batter into the cream cheese layer.
Bake the brownies for 35 minutes. Let the brownies cool completely in the pan before cutting and serving.
Notes
Homemade pumpkin pie spice is easy to make, but you can also use store-bought.Block-style cream cheese is a must for baking. The kind that's sold in the plastic tub isn't as thick and tends to lose its structure after baking. I do not recommend low-fat for the same reason.Store covered in the refrigerator for up to 5 days.Freeze for up to 2 months. Covered in plastic wrap and aluminum foil to prevent freezer burn. Defrost in the refrigerator overnight before serving.