Preheat the oven to 350°F
Prepare a pie crust and bake it until golden, then let it cool
In a saucepan, whisk together sugar, cornstarch, and salt
Gradually whisk in milk
Cook over medium heat, stirring constantly, until thickened
In a bowl, whisk egg yolks
Slowly add some of the hot mixture to the yolks, whisking constantly
Return the yolk mixture to the saucepan
Cook for 2 to 3 minutes more, stirring constantly
Remove from heat and stir in butter and vanilla
Slice bananas
Arrange banana slices in the cooled pie crust
Pour the warm custard over the bananas
Cover the surface with plastic wrap and chill until set
Whip heavy cream with sugar and vanilla until soft peaks form
Spread or pipe whipped cream over the chilled pie
Chill before serving