Preheat your oven to 350°F (175°C). Spray a 9x13 rectangular baking dish with baking spray and line it with parchment paper.
Melt the bittersweet chocolate and the butter in a bowl in the microwave on 50 percent power for three to four 30-second increments. OR melt the butter and chocolate together in a heat-proof bowl over a pot of gently simmering water. Stir the melted chocolate and butter together until combined and set the mixture aside to cool slightly.
Beat together the sugar, eggs, and vanilla extract in a large bowl using your stand mixer or hand mixer until the mixture is smooth.
Add the flour, salt, and baking powder to the bowl with the egg mixture and stir just until combined.
Measure out 3/4 cup of the batter you've just created into a separate bowl and set it aside.
Add the chocolate mixture to the remaining batter and stir just until combined.
To the 3/4 cup of batter you set aside, add the oil, cinnamon, nutmeg, and pumpkin puree and stir to combine.
Dollop the chocolate brownie batter into the prepared pan and smooth it out as best you can with a silicone spatula or an offset spatula. Spoon the pumpkin batter over the brownie batter in little blobs and use a butter knife or a wooden skewer to swirl the two batters together to create a marble pattern on the top.
Bake the brownies for about 30 minutes at 350°F (175°C). When they've finished baking, the centre may still seem very slightly underdone.
It's a good idea to let the brownies cool just a bit (15-20 minutes) until they're set in the middle before slicing and serving.