Preheat your oven to 350°F (175°C) and grease a 9x9-inch baking pan.
In a medium bowl, mix the melted butter and granulated sugar until well combined.
Add the eggs one at a time, then stir in the vanilla extract.
In another bowl, whisk together the cocoa powder, flour, baking powder, and salt. Gradually stir this dry mixture into the wet ingredients until just combined.
In a separate bowl, beat the softened cream cheese and powdered sugar until smooth and creamy.
Pour half of the brownie batter into the greased pan. Use a spatula to spread it evenly.
Drop spoonfuls of the cream cheese mixture on top of the brownie batter. Swirl it gently using a knife or toothpick to create a marbled effect.
Pour the remaining brownie batter over the cream cheese layer, spreading it carefully.
Bake in the preheated oven for 30-35 minutes or until a toothpick inserted in the center comes out mostly clean (a few crumbs are okay).
Let the brownies cool completely in the pan before cutting into squares.