In a large saucepan, combine milk, granulated sugar, cornstarch, and salt over medium heat, stirring frequently until thickened.
Meanwhile, mash one over-ripe banana in a small bowl, and set aside.
In a small bowl, lightly beat two eggs.
When the milk and sugar mixture has thickened, it's time to temper the eggs by adding about 3 tablespoons of the hot milk mixture into the eggs, stirring to combine. Set aside.
Add the mashed bananas into the saucepan, stirring to combine, and then add the tempered eggs into the saucepan, stirring well to combine.
Bring the mixture to a gentle boil and cook, stirring occasionally, for an additional 2 minutes. Remove from heat.
Add the vanilla extract to the banana mixture, and stir to combine. Cool for 15 minutes.
Pour the cooled mixture into a bowl, cover the banana cream with a layer of plastic wrap, and store it in the refrigerator, if needed, until ready to assemble the pie.
Slice 2 bananas and place half of the slices on the bottom of a pre-baked pie crust.
Spoon half of the cooled banana cream mixture over the sliced bananas.
Top with another layer of sliced bananas, and top with the remaining banana cream mixture.
Cover the pie with a plastic wrap layer and chill in the refrigerator while making the whipped cream topping.