Preheat your oven to 350°F (175°C) and prepare a 9x13-inch baking pan by greasing it or lining it with parchment paper.

In a large mixing bowl, combine melted butter, granulated sugar, and brown sugar. Mix until well combined. Add eggs one at a time, mixing well after each addition, then stir in vanilla extract.

In another bowl, whisk together flour, cocoa powder, salt, and baking powder. Gradually add this dry mixture to the wet ingredients and mix until just combined.

In a separate bowl, beat cream cheese with powdered sugar until smooth. Add egg and vanilla extract, mixing until well combined.

Pour half of the brownie batter into the prepared baking pan. Spoon dollops of the cheesecake mixture over the brownie layer, then pour the remaining brownie batter on top. Swirl the cheesecake mixture into the brownie batter for a marbled effect.

Bake in the preheated oven for 30-35 minutes. Check for doneness by inserting a toothpick into the center; it should come out with a few moist crumbs.

Allow the brownies to cool in the pan for 15-20 minutes, then transfer to the refrigerator and chill for at least 120 minutes before cutting into squares.