Beat pudding mix and milk in large bowl with whisk. Refrigerate 10 minutes to set.
Arrange 10 graham squares, slightly overlapping, on bottom of 8-inch square pan; set aside. Stir thawed cool whip topping into pudding. Spread half the pudding mixture over graham squares in pan; top with layers of 10 of the remaining graham squares, remaining pudding mixture and remaining graham squares.
Mix the pumpkin pie spice into the frosting and frost the cake. Optional: crush one more gingerbread graham cracker very fine to add a finishing touch to the top of the cake. Refrigerate 3 hours.