In a saucepan, combine sugar, flour and salt. Add milk in gradually while stirring gently. Cook over medium heat, stirring constantly until the mixture is bubbly. Keep stirring and cook for about 2 more minutes, and then remove from the burner.

Stir a small quantity of the hot mixture into the beaten egg yolks, and immediately add egg yolks mixture to the rest of the hot mixture. Cook for 2 more minutes; remember to keep stirring. Remove the mixture from the stove, add butter and vanilla. Stir until the whole thing has a smooth consistency.

Slice bananas into the cooked baked pastry shell. Top with pudding mixture.

Bake at 350°F for 12 to 15 minutes. Chill for an hour.