For the filling:
Two 14-oz cans sweetened condensed milk, labels removed
2 cups heavy cream
3 tablespoons confectioners’ sugar
1 vanilla bean, split lengthwise
3 tablespoons finely grated bittersweet chocolate
For the crust:
1 ½ cups all-purpose flour
½ cup confectioners’ sugar
1 stick (8 tablespoons) unsalted butter, cut into ¼ inch pieces and chilled
¼ teaspoon kosher salt
2 large egg yolks, lightly beaten
a 10 inch fluted nonstick tart pan with a removable bottom; parchment paper
Make the caramelized milk:
Put the cans of condensed milk in a large pot and cover them generously with water. Bring the water to a boil and boil for 4 hours. Be sure the water is boiling and the cans are covered with water the entire time (this is very important)—add more boiling water to the pot if the water level threatens to get too low. Remove the cans from the pot and let them cool completely; keep them in the fridge until you’re ready to use them.
Make the crust:
Sift the flour into a food processor, and then add the sugar butter and salt. Pulse until the mixture looks like fine breadcrumbs. Add the yolks and pulse until crumbly dough forms. Scrape the dough out onto a work surface and lightly knead just until smooth. Form the dough into a ball, wrap it in plastic wrap, and refrigerate it for at least 2 hours or up to 2 days.
Preheat oven to 350F.
Cut the chilled dough into 2 or 3 large pieces and grate it on the large holes of a box grater. Use your fingers to press the dough onto the bottom and up the sides of the tart pan to create an even layer, the bottom about ¼ inch thick and the sides about ½ inch thick. Work swiftly you don’t want the dough to warm up too much. Gently prick the bottom here and there with a fork, and then pop the pan into the freezer for 15 minutes. Cut out a 13 in circle of parchment paper and line the dough with it. Fill the tart shell with raw rice or dried beans and set the pan on a baking sheet. Bake the tart shell until the rim is light golden brown, 15 to 20 minutes. Remove the parchment paper and the rice or beans and bake until golden brown all over about 15 minutes more.
Assemble the pie:
Peel half of the bananas and slice them on the bias into approximately ½ inch thick pieces. Starting from the outside and working your way to the enter, arrange half of the bananas in concentric circles on the bottom of the tart shell, so each piece overlaps slightly. Gently dollop the caramelized condensed milk on top of the bananas, and spread it evenly over the slices. Cover with plastic wrap and put it in the fridge to chill, up to 2 hours.
While the pie is chilling, combine the cream and the confectioners’ sugar in a bowl. Use a knife to scrape the vanilla bean seeds into the cream; discard the pod. Use whisk or a handheld electric mixer to whip the cream to soft peaks. Cover it too, and chill in the fridge.
Peel and slice the remaining bananas. Add another layer of bananas. Give the whipped cream a good, brief whisk, and then spread it over the pie so it completely covers the bananas. Sprinkle the grated chocolate over the top.
Serve straightaway, when it’s still good and cold.