Stir sugar, cornstarch, and salt together in a large saucepan. In a small bowl, whisk the egg yolks till smooth. Gradually whisk in the milk; mix well. Slowly stir the milk mixture into the saucepan, whisk together.

Cook over medium heat, stirring constantly, till mixture thickens and boils. Boil and stir for 1-2 more minutes. Remove from heat and stir in butter and vanilla. (If desired, pour through a metal strainer to remove any lumps.)

Place saucepan in an ice water bath to cool the pudding. ( I usually fill my sink with 2-3 inches of ice water and place the pan in it.) Stir often to prevent a skin from forming on the top of the pudding.

Slice the bananas into the pie shell. Pour the lukewarm pudding over the bananas. Chill for at least 2 hours.

Whip the cream till soft peaks form. Whip in the powdered sugar and vanilla. Spread on top of the chilled pie. Serve immediately.