Pulse flour, salt and sugar in a food processor until comvbined. Add butter, and process, until combined. Add butter and process until mixture resembles coarse meal, about 1o seconds. WEith the machine running, add ice water in a slow, steady stream until mixture just begins to hold together.
Shape dough into two disks. Warp each in plastic, and refrigerate until form, about 1 hour, or up to 2 days.
On al lightly floured work surface, roll pate brisée to 1/8-inch thickness. Fit into a 9-inch pie dish. Trim edges, leaving a 1-inch overhang. Tuck overhand under dough so edges are flush with rim and crimp edges. Lightly prick bottom of dough eith a fork. Refrigerate for 30 minutes.
Preheat oven to 375°F Line dough with parchment, and fill with pie weights or dried beans, Bake until edges begin to turn gold, 15-18 minutes. Carefully remove weights and parchment. Bake until bottom and sides are goldenm brown, 12-15 minutes. let cool completely on wire rack. Crust can be stored overnight.
Combine sugar, cornstarch and salt in a medium saucepan. Whisk in milk and vanilla seeds, and cook over medium-high heat, stirring constantly, until bubbling and thick, about 7 minutes, about 2 minutes after it comes to a boil.
Whisk yolks in a medium bowl umtil combined. pour in milk mixture in a slow, steady stream, whisking until completely incorporated. Return mixture to saucepan, and cook over medium heat, stirring constantly, until it returns to a boil, 1-2 minutes.
Remove from heat and stir in 1/4 cup rum. Add butter, 1 tablespoons at a time, whisking until butter melts, before adding the next piece. Let cool in saucepan on wire rack, for about 10 minutes.
Pour custard into piecrust. Press plastic wrap directly on surface of custard. Refrigerate until custard filling is chilled and firm, at least 4 hours or overnight.
Meanwhile, place cream and vanilla pod in a bowl. Cover, and refrigerate for at least 4 hours or overnight.
Just before serving, remove vanilla pod from cream, and discard. Whisk cream until soft peaks form. Add confectioner's sugar and remaining tablespoons rum, and whisk until stiff peaks form. Transfer to a pastry bag fitted with a 1/2 inch star tip, such as Ateco #3826, and pipe whipped cream over pie. Serve immediately.