Preheat oven to 425°.
To prepare the crust, lightly spoon the flour into dry measuring cups, and level with a knife. Combine 1/4 cup flour and water, stirring with a whisk until well-blended.
Combine 3/4 cup flour, 2 tablespoons sugar, and 1/8 teaspoon salt in a bowl; cut in shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Add slurry; mix with a fork until flour mixture is moist.
Press the mixture gently into a 4-inch circle on heavy-duty plastic wrap; cover with additional plastic wrap. Roll dough, still covered, into a 12-inch circle. Freeze 10 minutes.
Remove 1 sheet of plastic wrap; fit dough into a 9-inch pie plate coated with cooking spray. Remove top sheet of plastic wrap. Fold edges under; flute. Line dough with a piece of foil; arrange pie weights or dried beans on foil. Bake at 425° for 20 minutes or until edge is lightly browned. Remove pie weights and foil. Reduce temperature to 350°. Bake an additional 5 minutes; cool on a wire rack.
To prepare filling, combine 3/4 cup sugar, cocoa, cornstarch, 1/8 teaspoon salt, and milk in a medium saucepan; stir well with a whisk. Cook, stirring constantly, for 1 minute until mixture comes to a full boil. Gradually add 1/3 cup hot milk mixture to beaten egg; stir well. Return egg mixture to pan. Cook 2 minutes or until mixture thickens, stirring constantly. Remove from heat; add grated chocolate, stirring until the chocolate melts and mixture is smooth. Stir in vanilla. Spoon mixture into pastry crust. Cover surface of filling with plastic wrap. Chill until set (about 2 hours). Remove plastic wrap; spread whipped topping evenly over filling.