Bake pie shell. Stir together sugar, cornstarch, and salt in saucepan. Blend milk and egg yolks; gradually stir into sugar mixture. Cook over medium heat, stirring constantly, until mixture thickens and boils. Boil and stir 1 minute. Remove from heat; blend in butter and vanilla. Press plastic wrap onto filling in saucepan and cool to room temperature.
Peel and slice bananas; arrange layer of banana slices 1/2 inch deep in baked pie shell. Pour over cooled filling.
Chill pie thoroughly, at least 2 hours (preferably overnight). Just before serving, top pie with sweetened whipped cream.