Prep the pan: Line a 9x13-inch baking dish with a single layer of graham crackers.
Break pieces as needed to cover the bottom with no big gaps.
Mix the pudding: In a large bowl, whisk the instant pudding and cold milk for about 2 minutes until thick but still spreadable. Let it sit for 1–2 minutes to fully set.
Fold in the whipped topping: Gently fold in the thawed whipped topping (or your freshly whipped cream) until the mixture is smooth and fluffy. Don’t overmix.
Build the first layers: Spread half of the pudding mixture over the graham crackers.
Add another layer of crackers on top, lining them up edge to edge.
Add the second filling layer: Spread the remaining pudding mixture evenly. Top with a final layer of graham crackers to create a neat “lid.”
Make the chocolate glaze: In a small saucepan, heat heavy cream and butter over medium-low until steaming and the butter melts. Pour over the chocolate chips in a bowl.
Let sit 2 minutes, then add a pinch of salt and vanilla. Stir until silky and smooth. (Microwave option: microwave cream and butter until hot, then proceed the same way.)
Glaze the cake: Pour the warm glaze over the top cracker layer. Tilt the pan or use an offset spatula to spread it to the edges in an even layer.
Chill: Cover the dish with foil or plastic wrap.
Refrigerate for at least 6 hours, ideally overnight, so the crackers soften and flavors meld.
Slice and serve: For clean slices, use a sharp knife warmed under hot water and wiped dry between cuts. Serve cold.