Set a heatproof bowl over a saucepan of simmering water. Melt chocolate and butter, stirring until smooth. Remove from heat and whisk in sugar. Add eggs one at a time, whisking until glossy and fully incorporated. Whisk in cocoa powder, vanilla, flour and salt just until smooth.

In a medium bowl, whisk cream cheese until completely smooth. Add eggs, vanilla and sugar, whisking until fluid and lump-free.

Spread half the chocolate batter in the pan. Spoon over half the cheesecake mixture and smooth lightly. Top with remaining chocolate batter. Dollop remaining cheesecake mixture over the surface and swirl with a knife to marble.

Bake until the edges are set and the center is slightly soft but not liquid, 22 to 28 minutes. A toothpick inserted in the center should come out with moist crumbs.

Transfer to a rack and cool completely in the pan. Refrigerate until fully set before slicing for clean edges.