Stir together your dry pudding mix and milk in a large bowl for about 2 minutes till it starts to thicken.
Carefully fold in 1/2 cup of cool whip until mixed throughout.
Place a layer of graham crackers, into the bottom of a 9x13 pan. Set the graham crackers side by side to cover the whole bottom of the pan. Break graham cracker pieces as needed to fill the whole pan.
Slice up banana and spread an even layer of sliced bananas (about 1 1/2 bananas worth) over the top of the graham crackers.
Carefully spread half of the pudding mixture over the top of the bananas and graham crackers. Spread evenly to the edges.
Place another layer of graham crackers to cover completely.
Add more banana slices and more pudding spread evenly.
Add final layer of graham crackers, placed evenly over the pudding.
Spread remaining cool whip over the top of the final layer of graham crackers, evenly to the edges.
Cover the cake with plastic wrap and set in the fridge for 4 hours, up to overnight.
**Or place ice box cake in the freezer. Remove from freezer and allow to come to room temperature for about 15 minutes before serving.
Slice and serve.
Banana icebox cake will stay good in the fridge or freezer for up to 4 or 5 days. Graham crackers will become more soft as the more time passes.