Preheat your oven to 375°F (190°C). Roll out the dough into a 9-inch pie dish, trim edges, and prick the bottom with a fork. Bake for 15-20 minutes until golden brown. Cool completely.

In a saucepan, combine whole milk, granulated sugar, cornstarch, and salt over medium-low heat. Stir continuously until thickened and bubbling, about 8-10 minutes.

Lightly beat egg yolks in a bowl. Gradually add cup of hot pudding mixture while whisking. Pour back into saucepan with remaining pudding and continue stirring for 2-3 minutes, then remove from heat.

Add unsalted butter and vanilla extract to the thickened pudding, stirring until well melted. Let sit for 10 minutes to cool slightly.

Slice the bananas into rounds and layer them evenly on the cooled pie crust. Pour the warm pudding over the bananas and spread evenly.

Cover the pie with plastic wrap, pressing against the surface to prevent a film. Refrigerate for at least 4 hours until set.

Once chilled, remove the pie from the refrigerator. Top generously with whipped cream and garnish with extra banana slices or vanilla wafers before serving.