Preheat oven to 350°F (175°C) and line an 8×8-inch baking pan with parchment paper.
In a large bowl, whisk together melted butter and 1 cup granulated sugar.
Add eggs and 1 teaspoon vanilla, mixing until smooth.
Stir in cocoa powder, flour, salt, and baking powder until fully incorporated.
Spread the brownie batter evenly in the prepared pan.
In a separate bowl, beat the cream cheese and 1/3 cup granulated sugar until smooth.
Add egg and 1/2 teaspoon vanilla and beat until creamy.
Spread cheesecake mixture over brownie batter in the pan.
Drop spoonfuls of raspberry jam over the cheesecake layer.
Use a knife to swirl the jam into the cheesecake layer.
Top with fresh raspberries if using.
Bake for 35–40 minutes or until the edges are set and the center is slightly jiggly.
Cool in the pan for 30 minutes, then chill for at least 2 hours before slicing.