Preheat your oven to 425°F. In a food processor, pulse together the flour, sugar, and salt. Grate the cold butter into the mixture and drizzle in the ice water. Combine gently with a fork until a dough forms. Shape into a ball, wrap tightly in plastic, and chill for half an hour. On a floured surface, roll the dough into a circle about 2 inches wider than your pie pan. Drape the dough over your rolling pin and ease it into the pan, pressing it gently to fit without stretching. Trim the overhang to about 1 inch, tuck the edge under itself, and crimp decoratively using fingers or a fork. Line with parchment paper, ensuring the edges are frilled, then press foil against the paper to keep the crust’s shape. Bake for 15 minutes, then remove the foil, brush the crust with an egg wash made by whisking the egg with cream, and dock the bottom. Add foil around the edges and bake 10 minutes more at 425°F. Reduce the oven to 375°F and continue baking until the center is golden, about 15–20 minutes longer.

In a medium bowl, whisk the eggs and yolks together and set aside. Combine the sugar, cornstarch, and salt in a medium saucepan, whisk in the milk, and blend until smooth. Place over medium-high heat, whisking constantly until the mixture thickens, about 5 minutes. Reduce the heat to medium, stirring continuously for another 6 minutes before removing from the heat. Gradually pour a cup of the hot mixture into the eggs, whisking vigorously to temper them, then return the egg mixture to the pot, whisking over medium-high heat for 2 more minutes. Pour into a large bowl, add the vanilla and butter, and stir until fully incorporated. Cover the surface with plastic wrap and allow to cool to room temperature.

Combine the heavy cream, confectioners’ sugar, and vanilla in a stand mixer and whip on high speed until soft peaks form. This is best prepared just before serving but can be made ahead and chilled with the pie.

Spread a thin layer of the custard into the cooled pie crust. Arrange sliced bananas over the bottom, then pour or spoon the remaining filling over them, smoothing the top. Cover and refrigerate for a minimum of 4 hours. Just before serving, crown the pie with the whipped cream and garnish with fresh banana slices.