In a medium saucepan off of heat, whisk together the sugar, cornstarch, and salt. Then whisk in the egg yolks and the milk.
1 1/2 cups granulated sugar, 1/4 cup cornstarch, 1/2 teaspoon salt, 3 large egg yolks, 3 cups whole milk
Place over medium heat and stir consistently until it is boiling and thickened, about 10 minutes. Once it starts to boil and you see big bubbles, let it boil, while stirring, for 1 minute. At the end, it should be able to easily coat the back of a spoon.
Stir in the butter and vanilla until smooth.
1 tablespoon unsalted butter, 1 1/2 teaspoons vanilla extract
Add the sliced banana to the bottom of the baked pie crust. Pour the pudding mixture over the bananas. Depending on the size of your bananas, you may not use all of the pudding. Put the pie in the refrigerator to cool for 4 hours.
Make whipped cream before serving and pipe around the edges of the pie. Add some banana slices. Serve and enjoy!
1/2 cup whipped cream