Prepare the Chocolate Layer: In a medium saucepan, heat the 2 cups of milk and 1 cup of heavy cream over medium heat, stirring occasionally. Once it's warm but not boiling, remove from heat and whisk in the cocoa powder, powdered sugar, and vanilla extract until smooth and well combined. Stir in the chocolate chips until melted and fully blended.
Make the Cream Layer: In a separate mixing bowl, whip the remaining 1/2 cup of heavy cream until it forms soft peaks. Gently fold in the marshmallow fluff until fully incorporated, creating a fluffy and light cream layer.
Layer the Lasagna: In a rectangular glass dish, lay down 4 sheets of chocolate graham crackers as the base. Pour half of the chocolate mixture over the crackers, spreading it evenly. Layer on 4 more sheets of graham crackers, followed by half of the cream mixture spread over that layer.
Repeat the Layers: Continue this process, adding another layer of chocolate graham crackers, followed by the remaining chocolate mixture and the final layer of graham crackers. Top with the remaining cream layer, spreading it evenly over the top.
Chill: Cover the dish with plastic wrap or foil and refrigerate for at least 4 hours, preferably overnight, to allow the layers to set and meld together.
Finish and Serve: Just before serving, sprinkle crushed candy canes on top for a festive crunch, and add mini marshmallows for garnish. Cut into squares and serve chilled or at room temperature.