Prepare the brownie base:
Preheat your oven to 350°F (175°C). Line an 8×8-inch baking pan with parchment paper, leaving overhang for easy removal. Melt the butter and chopped dark chocolate together in a heatproof bowl over simmering water or in short bursts in the microwave. Stir until smooth and set aside to cool slightly.

Mix sugars and eggs:
In a mixing bowl, combine brown sugar, granulated sugar, eggs, and vanilla extract. Whisk together until smooth and slightly thickened.

Combine chocolate and egg mixtures:
Slowly pour the melted chocolate mixture into the sugar and egg mixture, stirring continuously until fully combined.

Add dry ingredients:
Sift together flour, Dutch-processed cocoa powder, and salt. Fold these dry ingredients into the wet mixture gently until no streaks remain. Do not overmix.

Prepare the cheesecake layer:
In a separate bowl, beat the softened cream cheese with sugar until smooth and creamy. Add the egg, vanilla extract, and sour cream and beat until combined. Gently fold in the raspberry compote, leaving some swirls for marbling.

Layer the batter:
Pour half of the brownie batter into the prepared pan and spread evenly. Dollop half of the cheesecake mixture over the brownie batter in spoonfuls. Add the remaining brownie batter on top, followed by the rest of the cheesecake mixture.

Create swirls:
Using a knife or skewer, gently swirl the two layers together to create a marbled effect, taking care not to overmix.

Bake:
Bake in the preheated oven for 35-40 minutes, or until the edges are set but the center still slightly jiggles. A toothpick inserted into the brownie portion (not the cheesecake) should come out with moist crumbs.

Cool and serve:
Allow the brownies to cool completely in the pan on a wire rack before slicing. Chill in the fridge for firmer slices if desired.