Using a food processor, mix the shortbread with a pinch salt; process in long pulses until finely ground and beginning to stick to the sides. Add the melted butter and pulse just until incorporated. Transfer the crumbs to a 9-inch pie plate and press evenly into the bottom and up the sides. Freeze the pie shell.
Place 2 oz. chocolate in a small bowl and set aside. In a heavy saucepan, whisk together the milk, granulated sugar, cornstarch and remaining salt. Whisk in the egg yolks over medium-high heat until the custard boils and is very thick, about 5 minutes. Remove from the heat, measure out 1/2 cup of the hot custard and add to the bowl of chocolate; let sit for a minute (the chocolate will melt by itself). Meanwhile, whisk the remaining 2 tbsp. (cold) butter into the custard in the saucepan. Stir in the rum and transfer the rum custard to a heatproof bowl. Refrigerate until well chilled, stirring occasionally, about 2 hours.
Meanwhile, stir the chocolate custard, then stir in 1 tbsp. cream and the vanilla. Remove the pie shell from the freezer and spread the chocolate custard across the bottom. Refrigerate to firm up.
Working over the pie shell, cut the bananas into 1/4-inch thick slices, letting them fall to cover the bottom. Spoon the rum custard over the bananas, smoothing the top. Refrigerate for 2 hours to set.
Whip the remaining cream with the confectioners sugar until it forms soft peaks. Spread on top of the rum custard and refrigerate for at least 20 minutes or until serving time.
Just before serving, using a vegetable peeler, shave curls off the remaining 1 oz. chocolate onto the top of the pie.