Make the crust:
Preheat oven to 350 degrees F.
Melt butter and sugar together in a saucepan over medium heat. Gradually add cookie crumbs and stir to combine well. Press crumb mixture onto the bottom and up the sides of a 9-inch pie dish. Bake crust 10 to 12 minutes. Cool completely.
Heat the milk over medium heat until warmed, but not boiling. Beat the yolks in a large bowl. Slowly whisk the warm milk into the yolks and add the vanilla. Whisk sugar, cornstarch, and salt together in heavy medium saucepan. Over medium heat, gradually whisk in the egg, milk, and vanilla mixture to the dry ingredients until custard thickens and you can see the tracks from the whisk in the bottom of the pan, about 6 minutes. Remove from heat. Transfer custard to large bowl and fold in bananas; cover bowl with plastic wrap and cool custard completely in refrigerator, about 1 1/2 hours.
When custard has chilled, make topping by whipping cream with sugar and vanilla in a mixer at high speed until soft peaks form. Fold in most of the remaining chocolate cookie crumbs, reserving a few for garnish.
Stir custard to loosen, if necessary. Spread over bottom of prepared crust. Top with whipped cream mixture. Refrigerate until ready to serve. Scatter remaining chocolate crumbs over top just before serving.