Arrange the banana slices in 2 snug layers across the bottom of the cooled crust.
Whisk the milk, granulated sugar, cornstarch, salt and egg yolks in a heavy saucepan.
Cook over medium heat, whisking constantly, until the custard bubbles, then boil for 1 minute.
Remove from the heat, stir in the butter and vanilla, pour the warm custard over the bananas, and press parchment on the surface.
Refrigerate for 5 hours, then beat the cream and powdered sugar to soft peaks and spread it over the chilled filling.