Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan or line it with parchment paper for simple removal of the brownies later.
In a medium saucepan, melt the unsalted butter over low heat. Once fully melted, remove it from the heat and mix in the granulated sugar until the mixture is smooth and well combined.
Add the eggs one by one to the butter-sugar mixture, beating well after each addition. Pour in the vanilla extract and stir until fully incorporated.
In a separate bowl, sift together the all-purpose flour, cocoa powder, and fine salt. Gradually incorporate this dry mixture into the wet ingredients, folding gently with a spatula until just combined. Avoid overmixing for the best texture.
Pour about two-thirds of the brownie batter into the prepared baking pan, spreading it evenly across the bottom using a spatula.
In a mixing bowl, beat the softened cream cheese until it becomes smooth and creamy. Gradually add the powdered sugar, mixing until thoroughly combined. Gently fold in the fresh raspberries or raspberry puree, creating swirls while being careful not to fully blend them.
Dollop the cheesecake mixture over the brownie layer, distributing it evenly. With a butter knife or skewer, swirl through the cheesecake and brownie layers to create a marbled effect.
Carefully pour the remaining brownie batter on top of the cheesecake layer and spread it evenly. You can create additional swirls with the knife for an attractive pattern on the surface.
Bake in the preheated oven for approximately 30-35 minutes. The brownies are done when the edges are set and a toothpick inserted into the center comes out with a few moist crumbs sticking to it.
Once baked, allow the brownies to cool completely in the pan on a wire rack. If you used parchment paper, you can lift the brownies out for easier cutting into squares.
Notes
For an elegant touch, garnish with extra fresh raspberries and a sprinkle of powdered sugar.