Make the dulce de leche: Place the unopened condensed milk can in a saucepan and add water until it comes halfway up the can. Bring to a boil over medium-high heat and cook for 3 hours, adding more water as necessary. Remove from the heat and let cool, 1 to 2 hours.
Preheat the oven to 350 degrees F (175 degrees C).
Make the pie: Stir graham cracker crumbs and melted butter in a mixing bowl until well blended. Press crumb mixture evenly into a 9-inch pie plate.
Bake in the preheated oven until lightly browned, 10 to 15 minutes. Remove pie crust from the oven and cool on a wire rack, about 10 minutes.
Open dulce de leche can and pour 1/2 of it (about 3/4 cup) over pie crust. Arrange 1/2 of the bananas in a single layer over dulce de leche. Repeat dulce de leche and banana layers once more.
Beat cream in a mixing bowl with an electric mixer until soft peaks form. Add sugar and vanilla; continue beating until stiff peaks form.
Spoon whipped cream over bananas. Chill pie for at least 1 hour before serving.