Preheat the oven to 350 degrees F. Cut a piece of foil 9 by 23-inches. Butter the corners and sides of a 9 by 9-inch baking pan. Line the pan with the foil, leaving an overhang on two sides. Fold the overhanging foil to make them doubly thick. (This will make it easier to lift the bar out of the pan.) For the topping: Whisk the coconut cream with the egg white and vanilla in a medium bowl. Toss the shredded coconut with the flour in another medium bowl. Stir the shredded coconut mixture into the coconut cream mixture. Set aside.
For the base: Whisk the flour with the cocoa powder and salt in a small bowl. Put the cookie dough on a clean work surface and dump the flour mixture on top. Knead the flour mixture and dough together until it is dark and homogenous. Sprinkle a little extra flour on the work surface, and use a rolling pin to gently press and roll the dough into a 7-or-8-inch square-don't worry if it cracks a bit. Put the dough in the prepared pan, using your fingers to press it evenly into the sides and corners. Scatter the coconut topping evenly over the base, making sure you cover the edges well and being sure not to press down so that the coconut mixture lies on top of the dough.
Scatter the chocolate on top and press it lightly into the coconut. Bake until the coconut is a toasted golden brown, the topping seems dry and a toothpick inserted in the center comes out clean, about 30 minutes. Cool completely on a rack before gently lifting out of the pan by the overhanging foil, about 20 minutes. Slice into 16 square bars.