In a large bowl, whisk the vanilla pudding mix with 1-¾ cups of the cold milk for 2 minutes. Fold in the thawed whipped topping until no white streaks remain.
Layer ⅓ of the graham cracker sheets into the bottom of a 13×9-inch baking pan. Top with half of the filling mixture. Repeat the layers and finish off with the remaining graham crackers.
In a medium microwave-safe bowl, combine the chocolate and butter. Microwave on high for 1 minute and stir. Then, microwave in 30 second intervals until the chocolate is melted. Add the confectioners’ sugar and remaining ¼ cup milk and mix well.
Spread the chocolate layer over the top layer of graham crackers. Refrigerate 4 hours or until set.
