Preheat oven to 400 degrees F. Spread 1 cup coconut on a baking sheet and bake 5 to 7 minutes or until golden, stirring once. Cool slightly. Transfer to a food processor. Process until finely ground; set aside.
In a large bowl combine the flour, sugar, baking powder, and salt. Using a pastry blender, cut in butter until mixture resembles coarse crumbs. Make a well in the center of the flour mixture; set aside.
In a medium bowl combine egg and 3/4 cup whipping cream. Add egg mixture all at once to flour mixture. Add toasted coconut and chocolate pieces. Using a fork, stir just until moistened.
Turn dough out onto a lightly floured surface. Knead dough by folding and gently pressing it for 10 to 12 strokes or until dough is nearly smooth. Pat dough into a 10x4-inch rectangle. Cut in half lengthwise and in sixths crosswise to make 12 rectangles.
Place rectangles 2 inches apart on an ungreased baking sheet. Brush wedges with additional whipping cream. Bake 13 to 15 minutes or until golden brown. If desired, top scones with additional shredded coconut the last 5 minutes of baking. Remove scones from baking sheet. Serve warm.