Preheat the oven to 350°F (175°C). Line the pie crust with parchment paper, and bake for 8-10 minutes.
In a medium saucepan, combine the condensed milk, water, cornstarch, vanilla extract, and salt. Heat over medium-high heat, whisking constantly, until thick and bubbly.
Remove from heat, and stir in the butter until melted. Let the filling cool slightly.
Spread the banana slices over the bottom of the cooled crust. Pour the filling over the bananas, and spread evenly.
In a medium bowl, whip the heavy cream until soft peaks form. Spread the whipped cream over the filling.
Chill the pie for at least 4 hours before serving.
Interesting Facts
Banana cream pie originated in the United States in the late 19th century.
Banana cream pie is sometimes topped with chocolate shavings or a drizzle of chocolate sauce.
The pie is usually served cold, but it can also be served at room temperature.