Preheat the oven to 350°F (175°C). Grease a 9×9 inch baking pan.
Brownie Layer: In a medium saucepan, melt the butter. Remove from heat, and stir in sugar, eggs, and vanilla. Beat in cocoa, flour, salt, and baking powder. Spread the batter into the prepared pan.
Cheesecake Layer: In a medium bowl, mix together the cream cheese, sugar, egg, and vanilla until smooth. Spread the cheesecake mixture over the brownie batter in the pan.
Swirl the layers together using a knife or skewer.
Bake for 35 to 40 minutes, or until brownies begin to pull away from the sides of the pan. Let cool in pan before slicing.
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