Prepare pudding with the milk in a large bowl and whisk to combine. Once thickened, carefully fold in 1/2 cup of the whipped topping until combined.
Place a layer of graham crackers on the bottom of a 9×13 pan, covering the bottom. Break graham cracker pieces as needed to fit.
Slice 1½ bananas crosswise and arrange the slices evenly over the top of the graham crackers.
Carefully top the banana layer with half of the pudding mixture, spreading evenly to the edges of the pan.
Place another layer of graham crackers on top of the pudding layer and spread evenly to cover completely. Top with the remaining 1½ banana slices.
Add a final layer of graham crackers, arranged evenly over the pudding layer. Spread remaining whipped topping over the top of the final layer of graham crackers, evenly to the edges.
Cover the cake with wrap and set in the fridge for 4 hours, up to overnight. Dust with cocoa if desired. Slice and serve. Keeps in the fridge for up to 2-3 days.
