For the brownie:
Preheat the oven to 170°C (325°F) Gas 3.
Put the chocolate in a heatproof bowl over a pan of simmering water (do not let the base of the bowl touch the water). Leave until melted and smooth.
Put the butter and sugar in a freestanding electric mixer with a paddle attachment and beat until all the ingredients are well incorporated.
Add the eggs one at a time, mixing well and scraping any unmixed ingredients from the side of the bowl with a rubber spatula after each addition.
Gradually beat in the flour, mixing well after each addition, then turn the mixer up to high speed and beat for a little longer until you get a smooth mixture.
Slowly pour in the melted chocolate and mix thoroughly. Pour into the prepared baking tray and smooth over with a palette knife.
For the cheesecake:
Put the cream cheese, sugar and vanilla extract in a freestanding electric mixer with a paddle attachment and beat on slow speed until smooth and thick. Add one egg at a time, while still mixing. Scrape any unmixed ingredients from the side of the bowl with a rubber spatula after each addition. The mixture should be very smooth and creamy.
The mixer can be turned up to a higher speed at the end to make the mix a little lighter and fluffier, but be careful not to overmix, otherwise the cheese will split. Spoon on top of the brownie and smooth over with a palette knife.
Bake in the preheated oven for 30–40 minutes, or until the cheesecake is firm to the touch and light golden around the edges. The centre should still be pale. Leave to cool completely, then cover and refrigerate for 2 hours, or overnight if possible.
For the cream topping:
Put the cream, sugar and raspberries in a freestanding electric mixer with a whisk attachment and beat until firm but not stiff.
Turn the brownie out onto a board and turn the right way up.
Spread the topping evenly over the brownie and decorate with more raspberries.