Preheat oven to 350°F / 180°C (or 170° fan assisted) and line a 9-inch square baking tray with parchment paper
Make the Brownie Batter
Whip eggs and sugar until light and thick, like custard.
Melt butter and chocolate together in the microwave at 30-second intervals.
Pour the chocolate and butter mix into the egg/sugar mix and mix until combined.
Fold in flour and salt until combined.
Set aside a small amount of the brownie batter for swirling on top (about ⅓ cup, or more if you want more brownie on top), then pour the rest of the batter into the prepared pan.
Make the Cheesecake
Place all the cheesecake ingredients in a bowl and cream together until smooth.
Pour the cheesecake mixture on top of the brownie batter in the pan. Add a few dollops of the reserved brownie mix on top and swirl those into the top of the cheesecake with a knife or spoon to make a pretty design.
Bake for 30 - 35 minutes or until the cheesecake just starts to turn golden at the edges. There should still be a wobble in the middle of the cheesecake. Bake for the minimum time for super gooey brownies, or bake for a few minutes longer for firmer brownies.
Let cool COMPLETELY before attempting to slice - seriously.
Notes
The quality of the chocolate really matters in this recipe, and you'll be able to taste the difference, so try to use a high-quality dark chocolate with at least 70% cocoa solids. For best results when slicing the cheesecake brownies, chill them in the fridge for an hour or so before slicing, then use a warmed knife to get super clean cuts - cleaning it off in between each slice.