In a large mixing bowl, whisk together the instant vanilla pudding mix and milk until smooth. Let it sit for about 5 minutes to thicken.
Gently fold in the 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 mixture.
Spread the remaining pudding mixture over the second layer of graham crackers.
Top with the final layer of graham crackers.
In a small saucepan over low heat, combine the chocolate chips, butter, corn syrup, and milk. Stir until melted and smooth.
Pour the chocolate mixture over the top layer of graham crackers, spreading it evenly.
Cover the dish with plastic wrap and refrigerate for at least 4 hours, or overnight for best results.