In a medium saucepan, whisk together the granulated sugar, cornstarch, and salt.
Gradually add the whole milk to the dry ingredients, whisking continuously to avoid lumps.
Place the saucepan over medium heat and cook, stirring often, until the mixture thickens (about 10 minutes).
In a separate bowl, whisk the egg yolks lightly.
Once the milk mixture has thickened, remove it from the heat. Slowly pour about 1 cup of the hot mixture into the egg yolks, stirring constantly to temper the eggs.
Pour the egg mixture back into the saucepan and return to low heat. Continue stirring for an additional 2-3 minutes until thickened.
Remove from heat, then stir in the vanilla extract and butter until fully combined.
Allow the custard to cool slightly for about 10 minutes, then stir in the sliced bananas.
Pour the banana custard into the pre-baked pie crust, smooth the top, cover with plastic wrap, and refrigerate for at least 2 hours.
Before serving, whip the heavy cream until stiff peaks form. Spread or pipe the whipped cream over the top of the pie.
Garnish with additional banana slices if desired, cut into slices, and serve chilled.