Place the cold milk into a large mixing bowl and add the two packages of instant chocolate pudding mix.
Whisk the mixture vigorously for 2 minutes, ensuring you reach the bottom corners of the bowl to incorporate all the powder. The mixture will begin to thicken significantly.
Use a rubber spatula to fold the 1 cup of whipped topping into the pudding until the color is uniform and the texture is lightened.
Pour the chocolate mixture into the prepared pie crust, smoothing the top with your spatula to create an even layer.
Cover the pie loosely with plastic wrap, ensuring the wrap does not touch the surface of the pudding.
Refrigerate for at least 3 hours, or until the filling is completely set and firm to the touch.
Slice with a sharp knife dipped in warm water for the cleanest edges and serve with additional whipped topping if desired.