Make the cheesecake batter. Blend cream cheese in a medium bowl with an electric hand mixer or spatula until smooth. Add sugar and vanilla and mix until very smooth glossy. Add egg and mix until well incorporated, then mix in sour cream. Set this aside.
Make the brownie batter. Combine chocolate and butter in a saucepan over very low heat and stir constantly until melted and smooth, or melt in the microwave at 50% power in short bursts with frequent stirring.
Combine eggs, sugar, vanilla and salt in a large bowl and whisk or beat with an electric hand mixer until pale and thick. Beat in warm melted chocolate mixture. Whisk together flour and cocoa powder and sprinkle it over the surface and fold it in until evenly combined. Reserve about ⅓ cup (80ml) of brownie batter and then spread the rest evenly into prepared pan using a small offset spatula .
Dollop the cheesecake batter over the brownie batter in the pan and spread it out in an even layer using a small offset spatula, then place teaspoons of reserved brownie batter randomly over top. I like to place 3 rows of 3 dollops for 9 dollops that span across the pan. Swirl it in with a knife to create a marbled effect.
Bake for 15 minutes. Reduce oven to 325°F and bake for another 15 minutes until puffed and the cheesecake is set in the middle with lightly golden edges. Transfer pan to a wire rack and let cool completely in the pan. Refrigerate for at least 1 hour before slicing with a hot dry knife.