For the crust: Preheat oven to 350 degrees. Add the sugar and melted butter to the crumbs and mix until well combined. Firmly press the crumb mixture into a 9-inch pie pan to form a crust on the bottom and sides. Bake for 8 minutes. Remove from the oven and chill until firm, about an hour.
For the filling: Sprinkle gelatin over the cold water and set aside. In a heavy saucepan, heat the milk over medium heat until just scalded.
Vigorously whisk together 1/2 cup sugar, cornstarch, and the egg yolks until completely mixed. Add a cup of the scalded milk to the egg mixture and stir constantly until combined. Pour the tempered milk-egg mixture back into the remaining milk in the saucepan.
Reduce the heat to medium-low and cook, stirring occasionally at first and then more constantly, until the mixture thickens and begins to gently boil, 12 to 15 minutes. Allow to boil for about one minute and then immediately remove from the heat.
Place the bittersweet chocolate in a small bowl. Measure out 1 cup of custard and pour over the chocolate. Add the vanilla extract and stir until the chocolate is completely melted and the mixture is smooth. Spread the chocolate custard over the bottom of the cooled piecrust. Place in the refrigerator to set, about 10 minutes.
Mix the softened gelatin and rum into the remaining custard, stirring vigorously until the gelatin completely dissolves. Allow the rum custard to cool to room temperature.
With an electric mixer, beat the egg whites until frothy. Add the cream of tartar and salt, then slowly add remaining 1/2 cup of sugar and continue to beat until soft peaks form.
Fold 1/3 of the egg whites into the rum custard until just combined; then gently fold in remaining whites until no yellow streaks remain. Gently pour the rum custard over the chocolate custard. (There may be extra custard.) Refrigerate until the filling is completely set, at least 3 hours.
For the topping: Before serving the pie, whip the cream. In a medium-sized bowl, beat the heavy cream with an electric mixer until foamy and starting to thicken. Add confectioners' sugar and continue to beat until soft peaks are formed. Dollop the whipped cream over the pie, garnish with a pile of chocolate shavings and serve immediately.
The piecrust and filling can be made the day before serving. Make the whipped cream the day of serving.