Preheat your oven to 350°F (175°C). Grease a 9x9 inch baking pan.
In a mixing bowl, combine melted butter and sugar. Add eggs one at a time, mixing well after each addition. Stir in cocoa powder, flour, salt, and baking powder until well combined. Pour into the prepared baking pan.
In another bowl, beat the cream cheese until smooth. Add sugar, egg, and vanilla extract, and mix until creamy. Spread over the brownie batter in the pan.
Bake for 35 minutes or until the cheesecake layer is set and a toothpick inserted into the brownie layer comes out clean. Allow to cool before cutting into squares.