Prepare the crust by combining crushed vanilla wafers, melted butter, and sugar in a bowl until the mixture resembles wet sand. Press firmly into a 9-inch pie dish, creating an even layer on the bottom and up the sides. Refrigerate for 30 minutes to set.
Make the pudding filling by whisking together sugar, cornstarch, and salt in a medium saucepan. Gradually whisk in milk until smooth, then heat over medium heat, stirring constantly until the mixture begins to thicken and bubble (about 5-7 minutes).
Temper the egg yolks by slowly adding about 1 cup of the hot milk mixture to the beaten egg yolks while whisking constantly. Pour this mixture back into the saucepan and cook for 1-2 more minutes until very thick, continuing to whisk constantly to prevent scorching.
Remove from heat and stir in butter and vanilla extract until completely melted and incorporated. Transfer to a bowl and cover with plastic wrap directly on the surface of the pudding (to prevent a skin from forming) and let cool for 15 minutes.
Assemble the base layers by arranging a layer of whole vanilla wafers on the bottom of the chilled crust, then top with sliced bananas (about 1½ bananas, sliced ¼-inch thick). Pour half of the pudding mixture over the bananas and spread evenly.
Create the second layer by adding another layer of vanilla wafers, remaining sliced bananas, and topping with the remaining pudding. Smooth the surface with a spatula and refrigerate while preparing the meringue.
Make the meringue by beating egg whites and cream of tartar in a clean, dry bowl until foamy. Gradually add sugar while continuing to beat until stiff, glossy peaks form (about 3-4 minutes). Fold in vanilla extract.
Top the pie with the meringue, making sure to spread it all the way to the edges of the crust to seal in the filling. Create decorative peaks with the back of a spoon.
Brown the meringue either under a broiler for 1-2 minutes (watching carefully to prevent burning) or use a kitchen torch to caramelize the surface until golden brown.
Chill thoroughly for at least 4 hours or overnight before serving to allow the pie to set completely for clean, beautiful slices.