Step 1

For the crust: Preheat the oven to 400˚. Roll the pie dough into a 13-inch circle on a lightly floured surface. Transfer the crust to a 9-inch-deep dish pie plate. Tuck the edges of the crust under to be even with the edge of the pie plate and crimp the edges as desired. Place the crust in the refrigerator for 1 hour (or freezer for 30 minutes). Line the inside of the crust with parchment paper, then fill with baking weights or dried beans. Bake for 16 to 18 minutes, until the edges of the crust are very lightly golden. Remove the pie weights and parchment paper and prick the bottom of the crust with a fork, 6 to 8 times. Return to the oven and bake until the whole crust is golden brown all over, 13 to 15 minutes longer. Let cool to room temperature.

Step 2

For the filling: Whisk together the sugar and cornstarch in a medium saucepan. Whisk in the half and half. Whisk the egg yolks in a separate medium bowl.

Step 3

Place the half and half mixture over medium heat. Cook until thickened, whisking constantly, 6 to 8 minutes. (Scrape the bottom and corners of the pot with a rubber spatula periodically, to make sure nothing gets stuck.) Remove from the heat.

Step 4

Remove 1 cup of the half and half mixture and slowly drizzle it into the egg yolks, while whisking constantly. Transfer the yolk mixture back to the pot and whisk to combine. Return to medium heat. Bring to a simmer and cook for 1 minute while it bubbles, whisking constantly, then remove it from the heat. Add the vanilla and butter and stir until everything is combined. Transfer to a medium bowl and press plastic wrap into the surface (to prevent a film from forming). Let cool slightly (about 15 minutes).

Step 5

Slice two of the bananas and spread them into an even layer over the base of the pie crust. Whisk the filling well then pour it into the pie crust and smooth the top. Press plastic wrap into the top of the pie to completely cover the filling. Refrigerate to cool completely, about 6 hours.

Step 6

For serving: Slice the remaining two bananas to decorate the top of the pie. Combine the heavy cream and confectioners sugar in a large bowl. Whisk with an electric mixer on medium-high speed until stiff peaks form, 2 to 4 minutes. Dollop the pie with the whipped cream, then slice and serve.