In a large mixing bowl, whisk together the instant vanilla pudding mix and cold milk. Continue whisking until the mixture thickens, about 2 minutes.
Fold in the whipped topping until fully combined to create a fluffy filling.
In a 9x13 inch baking dish, lay down a single layer of graham crackers to cover the bottom.
Spread half of the pudding mixture over the graham crackers, smoothing it out evenly.
Add another layer of graham crackers, followed by the remaining pudding mixture. Top with one more layer of graham crackers.
In a saucepan, combine the chocolate chips, butter, corn syrup, and vanilla extract over medium heat. Stir until melted and smooth.
Pour the chocolate glaze over the top layer of graham crackers, spreading it evenly to cover.
Cover the dish with plastic wrap and refrigerate for at least 4 hours or overnight for the best results.
Once set, slice into squares and serve chilled.