Fill the pan of your double boiler with water, place over high heat, and bring to a boil. In the bowl of your double boiler pour in the sweetened condensed milk. Reduce the heat to simmer, and then cook for 1.5 hours, stirring from time to time. (Remember to add more water to the bottom pan, when necessary, to keep the pan from burning.)
Bake pie crust according to manufacturer's instructions. Set aside. When the caramel is thick and darker, remove from heat and let cool slightly.
Slice the bananas into pie crust. Spread the caramel evenly over the bananas. Chill until cold (at least 4 hours).
Whip the cream with the sugar and vanilla until stiff peaks form. Spread the whipped cream over the bananas and serve.