Crush the cookies into fine crumbs by hand with a tart tamper, rolling pin, or in a food processor. Transfer the crumbs to a medium bowl with the powdered milk. Add the melted butter and heavy cream. Stir until the crumbs are evenly moistened. Transfer the crumb mixture to a pie plate and gently press it to cover the bottom and sides of the pan.
Transfer the pie plate to the preheated oven. Bake for 15 minutes. Remove the plate from the oven and allow the crust to cool to room temperature.
For the Custard Filling
In a medium saucepan, combine the egg yolks, sugar, brown sugar, cornstarch, and salt. Whisk the ingredients together until they form a thick, smooth mixture. Slowly add the milk, whisking to fully combine and prevent lumps from forming. Place the saucepan over medium heat and bring to a simmer, stirring often to prevent the mixture from scorching on the bottom of the pan. Simmer until the mixture is thick enough to coat the back of a spoon.
Remove the pan from the heat. Add the butter and vanilla and stir until the butter is melted and the mixture is smooth. Allow to cool slightly as you prepare the bananas, stirring occasionally to prevent a skin from forming on the surface.
Peel the bananas and slice into ½” thick slices. Arrange one third of the banana slices evenly on top of the cooled pie crust. Add half of the custard filling and spread it to the edge of the crust. Add another third of the banana slices followed by the remaining custard, spreading it to cover the banana slices. Add the last of the banana slices in a layer on top of the custard.
For the Chantilly Cream Topping
Place the cream and powdered sugar in the bowl of a stand mixer or a large mixing bowl. Using a whisk attachment for your stand mixer or beaters for a hand mixer, beat the cream and sugar on high speed until it forms stiff peaks.
Transfer the whipped cream to the pie, spreading it gently to evenly cover the banana slices. Chill the pie until you are ready to serve.