Make the crust: Pulse the flour, confectioners' sugar and salt in a food processor until combined. Add the butter and pulse until it is in pea-size pieces. Drizzle in 2 tablespoons cold water and pulse until the dough just comes together. Turn out onto a piece of plastic wrap; use the plastic to help form the dough into a disk. Wrap tightly and refrigerate until firm, at least 1 hour or overnight. (The dough can be frozen for up to 2 months; thaw at room temperature.)
Roll out the dough into a 12-inch round on a lightly floured surface. Ease into a 9-inch tart pan with a removable bottom; fold in the overhanging dough and press against the side of the pan. Chill at least 30 minutes.
Preheat the oven to 350 degrees F. Line the crust with foil and fill with pie weights or dried beans. Bake until golden around the edge, about 20 minutes. Remove the foil and weights and continue baking until the crust is golden all over, 10 to 15 more minutes. Transfer to a rack and let cool completely.
Make the filling: Put the chocolate in a medium bowl; set aside. Bring the half-and-half to a bare simmer in a small saucepan over medium heat (do not boil). Whisk the egg yolks, granulated sugar, vanilla and salt in a separate medium bowl. Gradually whisk the hot half-and-half into the egg mixture, then pour the mixture into the saucepan. Reduce the heat to medium low and cook, stirring, until thick, about 1 minute. Pour over the chocolate and let sit, undisturbed, 5 minutes. Add the butter and whisk until smooth. Pour the filling into the prepared crust and smooth into an even layer. Cover loosely with plastic wrap and refrigerate until set, about 2 hours.
Make the glaze: Whisk the confectioners' sugar, butter and rum in a small bowl. Drizzle over the tart. Let sit 5 minutes before serving.