In a medium sauce pan, mix sugar, cornstarch and salt, and then stir in milk gradually.
Cook over medium heat, stirring constantly, until mixture thickens and boils (will take a good 15 min or so). Boil for 1 minute and remove from heat.
Gradually stir at least half of the hot mixture into the eggs yolks. Then blend that back into hot mixture in saucepan.
Bring to a boil again and boil 1 minute more, stirring constantly.
Remove from heat, and blend in butter and vanilla.
Allow filling to cool.
Arrange a layer of sliced bananas 1/2" deep covering the bottom of the pie crust shell. Pour in cooled filling and smooth surface.
Keep pie in fridge. Serve with whipped cream.