Preheat your oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper or grease it well to prevent sticking. In a medium bowl, stir together the all-purpose flour, baking powder, and salt until combined. Set the dry mixture aside for later use.
In a medium sauce pot over medium heat, melt the butter. Continue to cook, stirring constantly, until the butter foams, develops brown specks, and gives off a nutty aroma. Remove from heat and let it cool slightly. Stir in the granulated sugar and vanilla extract until smooth. Next, beat in the eggs one at a time using a spoon, making sure each egg is fully incorporated before adding the next.
Gradually add the dry flour mixture from Step 1 to the butter-sugar-egg mixture from Step 2, stirring until the batter is evenly moistened. Once combined, divide the batter evenly between two large bowls, as you'll prepare two different flavors for marbling.
In one bowl of batter, blend in the unsweetened cocoa powder and miniature chocolate chips until fully incorporated, making a thick chocolate batter. In the second bowl, stir in the pumpkin puree and pumpkin pie spice until the mixture is smooth and evenly colored. I like to use fresh pumpkin puree whenever I can for an even richer flavor, but canned works great too.
Spread half of the chocolate batter (from Step 4) into the bottom of the prepared baking pan. Next, layer all of the pumpkin batter (from Step 4) over the chocolate layer. The chocolate batter will be thicker than the pumpkin batter. For the remaining chocolate batter, either spoon it on top or place it in a plastic bag, snip off the corner, and pipe it over the pumpkin layer in strips. Use a butter knife or spatula to gently swirl the two batters together to create a marbled appearance.
Bake the assembled brownie in the preheated oven for 40 to 45 minutes, or until the brownies begin to pull away from the sides of the pan and a toothpick inserted into the center comes out clean. Once done, cool the brownie completely in the pan before cutting into squares and serving. For neater slices, I recommend letting them cool for at least 30 minutes—this helps the marbled layers set perfectly.