Prepare the refrigerated dough for the crust per package instructions.
Prepare the Chocolate Filling: Microwave the chocolate and 1/2 cup butter in a microwave-safe bowl on HIGH for 30 seconds and then stir. Repeat this process until the chocolate is melted and smooth. It may take about 1-1/2 minutes.
Remove from microwave and 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. Bake at 350°F for 30 minutes. (Pie will be partially baked.)
Prepare the Coconut-Pecan Filling: In a medium bowl, whisk together brown sugar, corn syrup, 1/4 cup melted butter, 2 eggs, and 1 teaspoon vanilla until blended. Stir in pecans and coconut. Carefully spoon coconut-pecan filling over chocolate filling, starting at the outer edges, and return pie to oven. Bake until crust is golden and center is set, 35 to 40 minutes. Cover edge of pie crust with foil if necessary to prevent it from browning too much. Cool pie completely on a wire rack, about 3 hours.