Prep the pan and oven. Heat the oven to 350°F (175°C). Line the pan with parchment, leaving overhang for easy lifting. Lightly grease the parchment.

Melt chocolate and butter. In a heatproof bowl, melt the butter and chocolate together in the microwave in 20–30 second bursts, stirring between each. Cool for 3–4 minutes so it’s warm, not hot.

Mix sugars and eggs. Whisk granulated sugar, brown sugar, eggs, and vanilla into the melted chocolate. Whisk until shiny and slightly thick, about 30–45 seconds.

Combine dry ingredients. In a separate bowl, whisk flour, cocoa powder, and salt. Fold into the wet mixture until just combined. If using extra chocolate chips, fold them in now. Do not overmix.

Make the cheesecake batter. Beat cream cheese, sugar, egg yolk, vanilla, and a pinch of salt until smooth and creamy. Scrape the bowl to remove any lumps.

Assemble the layers. Spread about two-thirds of the brownie batter into the pan. Dollop spoonfuls of the cheesecake mixture evenly over the surface. Add the remaining brownie batter in small dollops between the cheesecake.

Create the swirl. Drag a knife or toothpick through the batters in gentle figure-eights. Make 3–4 passes. Don’t over-swirl or the layers blend and lose definition.

Bake. Bake for 28–35 minutes. The edges should be set, and the center should have a slight jiggle but not look wet. A toothpick inserted 2 inches from the edge should come out with a few moist crumbs.

Cool completely. Let the pan cool on a rack for at least 1 hour, then refrigerate for 30–60 minutes for cleaner slices. Lift out with the parchment and cut into squares with a warm knife.

Serve. Enjoy slightly chilled or at room temperature. The flavors deepen on day two.