In a large bowl, whisk together the two boxes of instant vanilla pudding mix and the cold milk. Continue whisking for 2 minutes until it begins to thicken. Gently fold in the thawed whipped topping until fully combined.

Arrange a single, even layer of graham crackers in the bottom of a 9x13-inch baking dish. Break crackers as needed to cover the entire surface.

Spread half of the pudding mixture over the graham crackers. Add a second layer of graham crackers, followed by the remaining pudding mixture. Top with a final, third layer of graham crackers.

In a medium saucepan over low heat, melt the butter. Whisk in the cocoa powder and salt until smooth. Remove from the heat and whisk in the powdered sugar and vanilla extract until glossy. If needed, add milk one tablespoon at a time until you reach a pourable consistency.

Immediately pour the warm chocolate glaze over the top layer of graham crackers. Use an offset spatula to spread it into a smooth, even layer.

Cover the dish with plastic wrap and refrigerate for at least 8 hours, or preferably overnight. This step is essential for the graham crackers to soften to a cake-like consistency.

Cut into squares and serve cold. Enjoy!