Heat your oven to 350ºF.
In a large bowl, combine the cookie crumbs and melted butter; stir to combine. Transfer 3/4 of the crumb mixture to a 9-inch pie pan. Form the sides of the pie crust by pressing the crumbs up the sides of the plate (it should be about 1/4 inch thick). Spoon the rest of the crumb mixture into the bottom of the plate; press it to form the bottom of the crust.
Bake 5-7 minutes, or until lightly browned. Remove from oven and let cool.
In a medium saucepan, whisk together the sugar, cornstarch, and salt. Add the milk and egg yolks; whisk until there are no lumps.
Turn the burner on to medium. Cook the pudding whisking constantly and scraping the bottom of the pot so it doesn't burn, until it begins to thicken and come to a boil – about 10 minutes. Let the pudding boil 1 minute; remove from heat.
Add the butter; whisk until the pudding is smooth. Thinly slice the bananas into the pudding; stir gently to incorporate.
Pour the banana cream into the cooled crust. Immediately cover with plastic wrap. Refrigerate until set (at least 4 hours).
Prepare the whipped cream by combining the cream, powdered sugar, and vanilla in the bowl of a stand mixer. Beat on high speed until thick and doubled in size – about 3 minutes.
Before serving, remove the plastic wrap and top the pie with whipped cream.