Have baked 9-inch pie shell ready.
In a large saucepan, scald the milk.
In another saucepan, combine the sugar, flour and salt; gradually stir in the scalded milk.
Over medium heat, stirring constantly, cook until thickened.
Cover and, 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.
If desired, make a meringue (you’ll have 3 leftover egg whites) to top the pie, or just let the pie cool until serving.