In a saucepan over medium heat, whisk together milk, sugar, cornstarch, and salt until smooth.
Cook and stir until the mixture thickens and comes to a boil. Reduce heat and continue cooking for 2 minutes longer.
Remove from heat, and stir a small amount into the egg yolks. Return all to the pan, whisking constantly.
Cook over medium heat until mixture thickens again and reaches 160°F. Remove from heat and mix in butter and vanilla.
Slice bananas into the pie crust. Pour hot filling over bananas. Press plastic wrap over filling.
Refrigerate for at least 3 hours. Top with whipped cream before serving.
Notes
For a more decorative touch, garnish with banana slices right before serving. To prevent bananas from browning, you can brush them with a bit of lemon juice.