Heat the oven to 350 degrees F and spray an 8x8-inch square baking pan with non-stick cooking spray. Line the pan with parchment paper or aluminum foil, leaving a 2-inch overhang on the sides and spray the paper or foil with non-stick cooking spray. Set aside.
In a medium bowl combine the flour, cocoa powder, baking powder, baking soda, salt, and sugar until evenly combined. Add the butter, egg, vanilla, and coconut extract and mix with a handheld electric mixer (or use a stand mixer) until the mixture is combined. Gently press or spread the dough evenly into the prepared pan. Set aside.
For the topping, cream together the cream cheese and butter in a medium bowl 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 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. The bars taste wonderful chilled, by the way.
Notes
Don't Overbake: they are best taken out of the oven when the edges are set and the center is still a bit jiggly. They will firm up after cooling but if they are baked too long, they will be hard and dry.