Preheat oven to 170°C (conventional oven) and line a 20x20cm square tin with aluminium foil. Lightly grease the foil with vegetable oil.
Melt butter in a large saucepan over low heat. Remove saucepan off heat and add chocolate. Let it sit for 2 minutes before whisking. Add sugars and whisk again - it's normal for it to look grainy. Set saucepan aside for 15 minutes cool slightly.
Place cream cheese into stand mixer bowl and whisk for 1-2 minutes. Add egg and and caster sugar and beat together for a few minutes until smooth.
In a small bowl, mix flour, salt and cocoa powder. Set aside.
Whisk in one egg at a time into chocolate batter until all four eggs are well incorporated. Whisk in vanilla extract and olive oil.
Add dry ingredients to the chocolate batter and whisk together well.
Pour chocolate batter into square tin. Spoon cream cheese batter on top and dollop spoonfuls of Barker's Mixed Berry compote around the tin. Use a knife or fork and drag it through cream cheese to create swirls.
Place in middle of oven and bake for 65 minutes or until the centre is just set when the tin is gently shaken. Start checking brownie after 50 minutes to ensure top is not over-browning. If it is, lightly cover tin with aluminium foil. Check every 5 minutes there in, depending on how wobbly centre is.
Remove from oven and allow to cool completely before attempting to slice. Rest in fridge for several hours if possible.