Heat the oven to 350°F (175°C). Line a 9 x 13-inch metal baking pan with parchment paper, leaving an overhang on the long sides, and lightly grease the parchment.

Whisk the melted, slightly cooled butter and sugar together. Add the eggs and vanilla, then whisk until the mixture is smooth.

In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt. Stir the dry mixture into the butter mixture just until no dry streaks remain.

Beat the softened cream cheese with the sugar until smooth. Mix in the pumpkin purée, egg yolk, pumpkin-pie spice, and vanilla.

Spread about two-thirds of the brownie batter into the prepared pan. Spoon the pumpkin mixture over the brownie layer, then dollop the remaining brownie batter on top.

Drag a knife through the batter several times to create broad swirls. Do not swirl too much, or the chocolate and pumpkin layers may blend together.

Bake for 35–42 minutes, until the edges are set and a toothpick inserted into the brownie portion comes out with moist crumbs. A little soft pumpkin filling on the toothpick is fine, but there should be no wet batter.

Cool the brownies completely in the pan for at least 1 hour before cutting. For cleaner slices, refrigerate the cooled pan for 30–60 minutes, then lift the brownies out using the parchment overhang.