Pour sweetened condensed milk into a large mixing bowl. Add 1 1/2 cups of ice water. Using an electric hand mixer or a stand mixer fitted with the whisk attachment, beat the water and milk together until well combined, about 1 minute.
Add the pudding mix and beat another 2 minutes until smooth.
Cover with plastic wrap and refrigerate at least 2 hours, up to overnight.
Pour the heavy cream into a large mixing bowl. Beat on high speed using a handheld mixer until stiff peaks form, about 6-7 minutes. Gently fold in the pudding little by little until well combined and you no longer see streaks of pudding.
Slice the bananas. In a large serving bowl or 6 individual bowls, layer the ingredients in the following order: vanilla wafer cookies, banana slices, pudding. Repeat the layers as necessary. Top with additional whipped cream, if desired.