Heat the oven to 350 degrees F. Line a 9x9 inch glass pan with foil, leaving a 2 inch overhang on either side. Spray the foil with cooking spray.
In a medium bowl combine the flour, cocoa powder, baking powder, baking soda, salt, and sugar until evenly combined. Add the butter, egg and vanilla and mix until the mixture is combined. Spread batter into prepared pan and set aside.
In a medium bowl, cream together the cream cheese and butter until light and smooth. Add the egg and mix well, then add the cocoa powder and vanilla and mix until well blended. Add the powdered sugar gradually while beating until the mixture is smooth. Fold in the coconut.
Dollop the topping evenly over the base and spread evenly.
Bake the bars for 30-35 minutes or until the edges are just set and the center is a little wobbly. Cool completely in the pan before lifting out and cutting into squares. Brownies can be eaten once cooled, but they are best refrigerated and enjoyed cold.