Preheat the oven to 330°F (165°C). Grease an 8x8-inch (20x20 cm) square baking tin with oil and line it with baking paper, leaving an overhang for easy removal.
In a heatproof bowl, melt the butter and dark chocolate together. Stir until smooth and set aside.
In a separate bowl, combine the cane sugar, light brown sugar, milk, and yogurt. Stir until the sugar dissolves completely.
Mix the melted chocolate mixture with the yogurt mixture until smooth and fully combined.
Add the dry ingredients (flour, cocoa powder, cornstarch, baking powder, and salt) to the wet mixture. Stir gently with a whisk until just combined—avoid overmixing.
Fold in the chocolate chips.
Pour the brownie batter into the prepared baking tin, leave some for topping.
Spoon dollops of cheesecake batter on top of the brownie layer, as shown.
Fill in the gaps between the cheesecake scoops with the remaining brownie batter.
Use a knife to make swirls if desired.
Bake for about 30 minutes, or until the brownie is evenly risen and the center is set.
Remove from the oven and let it cool completely for a couple hours or overnight. Once cooled, slice into portions and store in the fridge.