Preheat oven to 350 degrees. Line a 9 x 13 rectangular baking pan or dish with parchment paper or grease it with cooking spray.
Place the chocolate and the butter inside a heat-proof bowl. Fill a small saucepan halfway with water and bring it to a simmer over medium heat. Set a heatproof bowl over the saucepan melt the chocolate and butter while stirring occasionally until melted and smooth. Turn off the heat.
In a large bowl, whisk together flour, baking powder, and salt; set aside.
Using a hand mixer in a large bowl or stand mixer, mix the sugar, eggs, and vanilla, on medium speed until fluffy and combined, about 3 to 5 minutes.
Slowly add the flour mixture to the wet ingredients and mix to combine, stopping periodically to scrape the sides of the bowl.
Divide the batter between 2 medium bowls (about 2 cups per bowl). Add the chocolate mixture to one bowl and stir to combine.
To the non-chocolate mixture, add the pumpkin, oil, cinnamon, and nutmeg and stir to combine.
Pour the chocolate batter into the prepared pan and smooth the top with a rubber spatula. Next, pour the pumpkin batter over the chocolate in a semi-swirl way. With a small spatula gently swirl the two batters to create a marbled effect.
Bake for 35 to 40 minutes or until set and a toothpick comes out clean when inserted in the center of the pan.
Remove from the oven and allow the brownies to cool on a wire rack before cutting into 16 squares.
Notes
Swap the ¾ teaspoon pumpkin spice for 1 teaspoon cinnamon + ¼ teaspoon nutmeg.
Using a boxed brownie mix: you'll only need canned pumpkin and pumpkin spice. Follow the directions in the box to make the brownie batter. Then, divide it into two bowls. Add the pumpkin puree and spice to one bowl, then follow the swirl directions and bake. Since brownie mixes have the chocolate already in the entire mix, the swirl batter will be a dark brown, not a light orange, as when making it from scratch, but the flavor is there.