Combine the milk, sugar, and salt in a 1-quart saucepan over medium-low heat. Stir occasionally until the mixture begins to steam, about 5 minutes.
While the milk heats, whisk the heavy cream and cornstarch together in a small bowl until completely smooth with no lumps.
Slowly pour the cornstarch mixture into the warm milk, stirring constantly.
Reduce the heat to low and cook, stirring constantly, until the pudding thickens enough to coat the back of a spoon, about 5 minutes.
Remove from heat and stir in the butter and vanilla until the butter melts completely.
Pour the pudding into a small bowl. Press a piece of plastic wrap directly onto the surface to prevent a skin from forming. Let cool to room temperature.
Assemble the Pie
Line the bottom and sides of a small dessert dish or ramekin with vanilla wafers in a single layer.
Slice one banana and arrange the slices over the cookies.
Spoon the cooled pudding over the banana slices, spreading it to the edges to fully cover the fruit.
Cover and refrigerate for 1 to 2 hours until cold and set.
Top with whipped cream and extra banana slices before serving.
Notes
Use a small saucepan. A 1-quart saucepan keeps this small amount of pudding deep enough to stir properly. In a larger pan, the pudding spreads too thin and can scorch before it thickens.Cool the pudding before assembling. Spooning hot pudding over the banana slices will make them soft and mushy. Let the pudding cool to room temperature first so the bananas hold their shape.Press plastic wrap onto the pudding surface. Whether you're cooling the pudding in a bowl or chilling the assembled pie, press the wrap directly onto the surface. This prevents a thick skin from forming on top.Choose the right banana. A ripe banana with a yellow peel and just a few brown spots is ideal. Too green and the flavor will be starchy. Too brown and the slices won't hold their shape under the pudding.Chill long enough. The pudding needs at least 1 to 2 hours in the fridge to fully set. Cutting the chill time short means a loose, runny filling that won't hold together when you scoop into it.