Prepare the Crust:
If using a store-bought crust, bake it according to package instructions and allow it to cool. For a homemade crust, bake and cool completely before proceeding.
Make the Custard Filling:
In a saucepan, heat the milk over medium heat until warm (do not boil).
In a mixing bowl, whisk together sugar, cornstarch, and egg yolks until smooth.
Gradually add the warm milk to the egg mixture, whisking constantly to temper the eggs.
Return the mixture to the saucepan and cook over medium heat, stirring frequently, until thickened (about 5–7 minutes).
Remove from heat, stir in butter and vanilla extract until smooth.
Assemble the Pie:
Layer sliced bananas evenly on the bottom of the cooled crust.
Pour the custard over the bananas, spreading it evenly.
Cover the surface with plastic wrap to prevent a skin from forming and refrigerate for at least 4 hours or overnight.
Prepare the Whipped Cream:
In a mixing bowl, whip the heavy cream, powdered sugar, and vanilla extract until soft peaks form.
Decorate and Serve:
Spread or pipe the whipped cream over the chilled pie.
Garnish with additional banana slices if desired. Slice and serve chilled.