Whisk the pudding mix and cold milk in a large bowl for 2 minutes until thickened, then fold in the whipped topping.

Spread a thin layer of pudding in a 9x13-inch dish, then arrange a single layer of graham crackers to cover the bottom.

Spread half the remaining pudding over the grahams, add another layer of graham crackers, then spread the rest of the pudding, and finish with one final layer of grahams.

Microwave the frosting until pourable, spread it over the top graham layer, cover loosely, and refrigerate at least 4 hours.

Run a hot knife under water, dry it, and slice the cake into squares. Serve chilled.