Prepare the Crust: Stir together 1 1/2 cups flour, 1/2 tablespoon granulated sugar, and 1/2 teaspoon salt in a large bowl. Using a pastry blender, cut butter and shortening cubes into flour mixture until mixture resembles small peas. Using a fork, gradually stir in 4 tablespoons ice water, stirring until dry ingredients are moistened and dough begins to form a ball and pulls away from sides of bowl, adding up to 1 more tablespoon of water, if necessary. Turn dough out onto a work surface; shape and flatten into a disk. Wrap in plastic wrap, and chill 1 to 24 hours.

Preheat oven to 425°F. Unwrap chilled dough disk, and place on a lightly floured surface. Let dough stand at room temperature until slightly softened, about 5 minutes. Sprinkle dough with flour, and roll into a 13-inch circle. Fit dough into a 9-inch glass pie plate. Trim dough, leaving 1/2-inch overhang; fold edges under, and crimp. Prick bottom and sides 8 to 10 times with a fork. Freeze 20 minutes. Line piecrust with parchment paper, and fill with pie weights or dried beans. Bake in preheated oven 14 minutes. Remove weights and parchment paper, and bake until crust has lost its raw dough sheen, 5 to 7 minutes. Transfer to a wire rack, and cool completely, about 30 minutes. Reduce oven temperature to 350°F.

Prepare the Chocolate Filling: Microwave German’s sweet chocolate and 1/2 cup butter in a microwave-safe bowl on HIGH until melted and smooth, 1 to 1 1/2 minutes, stirring at 30-second intervals. Whisk in 3/4 cup granulated sugar, 3 tablespoons flour, and 1/8 teaspoon salt. Add 2 eggs, 1 at a time, whisking just until blended after each addition. Whisk in evaporated milk and 1 teaspoon vanilla until blended. Pour chocolate filling into prepared piecrust. Shield edges with aluminum foil to prevent excessive browning, and place on a rimmed baking sheet. Bake at 350°F for 30 minutes. (Pie will be partially baked.)

Prepare the Coconut-Pecan Filling: Whisk together brown sugar, corn syrup, 1/4 cup melted butter, 2 eggs, and 1 teaspoon vanilla until blended. Stir in pecans and coconut. Beginning at the outer edges of the partially baked chocolate filling, carefully spoon coconut-pecan filling over chocolate filling, and immediately return pie to oven. Bake until crust is golden and center is set, 35 to 40 minutes, shielding edges with aluminum foil to prevent excessive browning, if necessary. Cool pie completely on a wire rack, about 3 hours.

Prepare the Chocolate-Covered Pecans: Microwave chocolate chips in a small microwave-safe bowl on HIGH until melted, 30 to 45 seconds, stirring until smooth. Dip the lower half of each pecan into the melted chocolate, allowing excess chocolate to drip back into bowl, and place on a parchment paper-lined baking sheet. Chill until chocolate is firm, about 30 minutes. Arrange Chocolate-Covered Pecans decoratively around outer edge of pie. (You may have some left over.)