Preheat oven to 350-degrees F (175 degrees Celsius).
Place and crimp a 9" pie dough (homemade or store-bought) into a pie pan and dock the crust with a fork. Blind bake the crust (i.e. bake with no filling) for 20 minutes. Remove, cool, and set aside.
To make the banana cream pie:
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.
To make the whipped cream:
In the bowl of a stand mixer or a large bowl with a hand mixer, beat the heavy cream and 3 tablespoons granulated sugar until stiff peaks form.
Add 1 teaspoon pure vanilla extract to the whipped cream, and fold to combine.
Spoon the whipped cream topping over the banana cream pie and use an offset spatula to cover the pie with the whipped cream.
Refrigerate until ready to serve.
Notes
Store any leftovers, covered, in the refrigerator for up to 5 days.Pie may be frozen. Wrap well and store in the freezer for up to 3 months.Thaw in the refrigerator overnight.