In a large mixing bowl, whisk condensed milk, ice water, and instant vanilla pudding together until smooth. Refrigerate.
Use a handheld mixer (or a stand mixer fitted with whisk attachment) to whip heavy cream until soft peaks form. Carefully fold the whipped cream into the chilled vanilla pudding until well incorporated.
In one large dish (or in several small jars), layer the ingredients – vanilla wafers, vanilla pudding, and sliced bananas – repeating until you reach the top of the container.
Cover tightly, then refrigerate for at least 4 hours or up to 8 hours. If you let it sit longer, you risk the bananas browning a bit.
This made-from-scratch, southern dessert will easily feed a large group and is loved by all!