Make the chocolate layer: Whisk together the milk and pudding mix in a medium bowl and allow to firm up according to the instructions on the box.
Make the marshmallow layer: Beat the marshmallow creme and whipped topping in a large bowl with a mixer until smooth.
To assemble: Line the bottom of an 8-inch square baking dish with some of the graham crackers, breaking them up if needed to make a single layer. Spread half of the chocolate pudding evenly over the graham crackers. Add another layer of graham crackers to the dish and cover evenly with half of the marshmallow mixture. Repeat these layers ending with the marshmallow mixture on the top. Sprinkle with the shaved chocolate and refrigerate at least 4 hours before cutting and serving.