Preheat oven to 425 degrees. On a lightly floured work surface, roll out dough into a 14-inch round (1/4 inch thick). Fit dough into a 9-inch pie plate. Trim dough to extend above edges by 1 inch, fold under, and crimp. Prick bottom with a fork, and freeze until firm, about 15 minutes. Cut a large round of parchment paper (about 11 inches), and place in pie shell, allowing excess to extend above edges. Fill with pie weights. Freeze until cold, about 10 minutes.
Bake crust 15 minutes. Reduce oven temperature to 375 degrees. Remove pie weights and parchment, and bake until golden brown, about 20 minutes more. Let cool on a wire rack.
Make the filling: Combine granulated sugar, cornstarch, and salt in a bowl. Add egg yolks, and whisk until smooth. Bring milk to a simmer in a saucepan over medium heat. Add 1/2 cup milk to yolk mixture in a slow, steady stream, whisking constantly. Pour mixture into pan with hot milk, and cook, whisking constantly, until mixture begins to bubble and is very thick, about 6 minutes.
Pour milk mixture through a large-mesh sieve into a bowl. Add butter, and stir until melted. Fold in bananas. Pour into crust. Place plastic wrap directly on surface of filling to prevent a skin from forming. Refrigerate for 2 hours.
Make the topping: Beat together cream, sugar, and vanilla until soft peaks form. Spread whipped cream over filling. Using a rubber spatula or the back of a spoon, shape topping into peaks.
Using a vegetable peeler, shave chocolate at a 45-degree angle, and scatter over pie. (You will only need about 1 ounce of chocolate for the shavings, but it will be easier to shave if you start with a larger piece than you need.) Serve.