Heat your oven to 350 degrees F. Line an 8x8 inch baking pan with parchment paper, leaving a little overhang on two sides so you can lift the brownies out easily. Lightly grease any exposed pan edges.

Make the brownie batter. In a medium bowl, whisk the melted butter and 3/4 cup of the granulated sugar together until combined. Add both eggs and the vanilla extract and whisk again until the mixture looks slightly glossy, about 30 seconds. Add the flour, cocoa powder, salt, and baking powder and stir with a rubber spatula just until no dry streaks remain. Do not overwork it. Set the bowl aside.

Make the cream cheese layer. In a second bowl, beat the softened cream cheese and the remaining 1/4 cup sugar together with a hand mixer on medium speed until smooth and fluffy, about 1 minute. Add the pumpkin puree, cinnamon, and nutmeg and beat again until everything is combined and the mixture is a uniform orange color with no white streaks.

Spread about two thirds of the brownie batter into the prepared pan in an even layer. It will be thick, so use the back of a spoon or offset spatula to push it into the corners. Spoon the pumpkin cream cheese mixture over the top and spread it gently. Drop the remaining brownie batter in small spoonfuls across the surface of the cream cheese layer.

Swirl the layers using a butter knife. Drag the knife through the batter in slow S-shaped curves across the pan. Two or three passes is enough. If you swirl too much, the layers blend together and you lose the marbled look.

Bake for 28 to 32 minutes. The edges will pull away slightly from the pan sides and the center should not jiggle when you give the pan a gentle shake. A toothpick inserted in the center should come out with moist crumbs, not wet batter.

Let the brownies cool completely in the pan on a wire rack, at least 1 hour, before lifting them out and cutting into 16 bars. They firm up as they cool and will slice much more cleanly when fully cooled. Refrigerate any leftovers.