How to Make It
In a large bowl, whisk the flour with the confectioners’ sugar and salt. Using a pastry blender or 2 knives, cut in 1 stick plus 2 tablespoons of the butter until the mixture resembles coarse meal with some pea-size pieces of butter remaining. Stir in the cold water and egg yolk until the dough just comes together. Scrape the dough out onto a work surface and pat into a disk. Wrap the dough in plastic and refrigerate for 1 hour.
Preheat the oven to 350°. On a lightly floured work surface, roll out the dough to a 12-inch round, a scant 1/4 inch thick. Ease the dough into a 9-inch pie plate. Trim the overhang to 1 inch and fold it under itself. Crimp the edge and freeze until firm, about 15 minutes.
Line the crust with parchment paper and fill with pie weights or dried beans. Bake for about 20 minutes, until the crust is barely set. Remove the parchment and pie weights and bake for 20 to 25 minutes longer, until the crust is lightly browned; prick the bottom of the crust lightly to deflate it if it puffs up. Let cool.
In a medium saucepan, combine the remaining 1 stick of butter with the brown sugar and cook over moderate heat until the sugar is melted, about 5 minutes. Remove from the heat. Stir in the dulce de leche until smooth. Let the filling cool.
Meanwhile, in a microwave-safe medium bowl, microwave the chopped chocolate on high power in 10-second intervals until melted. Spread the chocolate over the cooled crust and freeze until firm, about 10 minutes.
Spread the dulce de leche filling in the crust and top with the sliced bananas. In a large bowl, using a hand mixer, beat the cream until firm. Pile the whipped cream on the pie and refrigerate for at least 3 hours, until the filling is set. Cut into wedges and serve.