Preheat your oven to 350°F (175°C). Line a 9x9 inch baking pan with parchment paper for easy removal and lightly grease it if not using parchment.
In a mixing bowl, melt the butter. Whisk in sugar until combined, then add eggs and vanilla extract, mixing well.
In another bowl, sift together cocoa powder, flour, salt, and baking powder. Gradually add dry ingredients into the wet ingredients, stirring until just combined. Do not overmix.
Pour half of the brownie batter into the prepared baking pan and spread evenly. Set aside the remaining batter.
In a separate bowl, beat the cream cheese until smooth. Add in sugar, egg, and vanilla extract, mixing until well combined. Gently fold in fresh blackberries.
Pour the cheesecake layer over the brownie base in the baking pan, spreading it evenly.
Drop spoonfuls of the reserved brownie batter on top of the cheesecake layer and swirl gently with a knife to create a marbled effect.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Remove from the oven and allow to cool in the pan on a wire rack. Once cooled, cut into squares and serve.