Prep the pan and oven. Heat the oven to 350°F (175°C). Line your pan with parchment, leaving overhang for easy lifting. Lightly grease the paper.
Melt chocolate and butter. In a heatproof bowl set over barely simmering water, melt the butter and semisweet chocolate, stirring until smooth.
Or microwave in 20–30 second bursts, stirring between each. Cool 5 minutes.
Make the brownie base. Whisk in granulated and brown sugars until glossy. Beat in eggs and vanilla until well combined and slightly thick, about 30 seconds.
Sift in flour, cocoa, and salt. Fold gently until just combined. Stir in extra chocolate chips if using. Do not overmix.
Make the pumpkin cheesecake swirl. In a separate bowl, beat cream cheese until smooth.
Add pumpkin puree, sugar, egg yolk, vanilla, spices, and flour. Mix until silky with no lumps. Taste and adjust spices to your liking.
Assemble. Spread about 2/3 of the brownie batter in the pan in an even layer.
Dollop spoonfuls of the pumpkin cheesecake mixture over the batter. Add remaining brownie batter in smaller dollops between the pumpkin patches.
Swirl. Use a butter knife or skewer to drag gentle figure-eights through the pan, swirling the two mixtures. Stop before it blends into one color. You want clear ribbons of pumpkin and chocolate.
Bake. Bake 30–38 minutes, depending on pan size and your oven. Start checking at 28 minutes.
The center should be set with a slight jiggle and a toothpick should come out with a few moist crumbs (not wet batter).
Finish and cool. If you like, sprinkle a pinch of flaky sea salt on top right after baking. Cool completely in the pan on a rack—at least 1 hour. For the cleanest slices, chill 30–60 minutes before cutting.
Slice and serve. Lift out using the parchment.
Use a warm knife (wipe between cuts) for neat squares. Enjoy at room temp or slightly chilled.