Turn out pate brisee onto a lightly floured work surface. Roll out to a 12-inch round, a bit less than 1/4 inch thick; fit into a 9-inch glass pie plate. Crimp edges as desired. Freeze until firm, about 15 minutes.
Preheat oven to 400 degrees. Line shell with parchment paper, leaving a 1-inch overhang. Fill with pie weights. Bake until edge of crust begins to turn golden, about 15 minutes. Remove parchment and weights. Reduce oven temperature to 375 degrees. Bake until pale golden, 15 to 20 minutes. Let cool on a wire rack.
Bring 3 cups cream almost to a boil in a medium saucepan. Remove from heat. Meanwhile, whisk together granulated sugar, eggs, egg yolks, and salt in a medium bowl. Slowly pour in hot cream, whisking constantly until combined; return cream mixture to saucepan. Cook over medium-low heat, stirring constantly with a wooden spoon, until mixture is thick enough to coat back of spoon and hold a line when you drag a finger through it, 10 to 12 minutes. Stir in rum. Remove from heat; set aside.
Separate any raisins that are stuck together. Arrange raisins in an even layer on bottom of cooled crust. Carefully pour in hot custard. Bake until center is set, 25 to 30 minutes. Let cool on a wire rack.
Before serving, put remaining 2/3 cup cream and the confectioners' sugar in the bowl of an electric mixer fitted with the whisk attachment. Beat on medium-high speed until soft peaks form. Serve pie with whipped cream.