Have a baked 9-inch pie shell ready.
In a large saucepan, scald the milk.
In another saucepan, over medium heat, combine the sugar, flour and salt; gradually stir in the scalded milk; stir constantly until thickened.
Cover; stirring occasionally, cook for two minutes longer.
In a small bowl, have the 3 egg yolks, slightly beaten, ready; stir a small amount of the hot mixture into beaten yolks; when thoroughly combined, stir yolks into hot mixture.
Cook for one minute longer; stirring constantly.
Remove from heat and blend in the butter and vanilla.
Let sit until lukewarm.
When ready to pour, slice bananas and scatter in pie shell; pour warm mixture over bananas.
Place in the refrigerator until ready to serve.
