In a large mixing bowl, whisk together the instant vanilla pudding mix and cold milk until smooth, about 2 minutes.
Gently fold in the thawed whipped topping until fully combined.
In a 9x13 inch baking dish, layer half of the graham crackers on the bottom.
Spread half of the pudding mixture over the graham crackers.
Add another layer of graham crackers on top of the pudding, followed by the remaining pudding mixture.
Finish with a final layer of graham crackers on top.
In a microwave-safe bowl, combine the chocolate chips and unsalted butter. Microwave in 30-second intervals, stirring in between, until melted and smooth.
Stir in the powdered sugar, milk, and vanilla extract until combined to create the glaze.
Pour the chocolate glaze over the top layer of graham crackers, spreading it evenly.
Cover the baking dish with plastic wrap and refrigerate for at least 4 hours or overnight for the best flavor and texture.
Before serving, slice into squares and enjoy.