Special equipment: a 9-inch glass pie plate
For the shortbread crust: Position an oven rack in the center of the oven, and preheat to 350 degrees F. Process the cookies, sugar, butter, rum and salt in a food processor until the texture of wet sand. Press the crumbs evenly into the bottom and up the side of a 9-inch glass pie plate. Bake until lightly browned, 8 to 10 minutes. Let cool completely on a wire rack.
For the sorbet filling: Mix the lime juice and rum in a measuring cup; set aside. Scoop 1 pint of the sorbet onto the bottom of the cooled crust, placing scoops evenly. Let stand until spreadable, about 5 minutes. Smooth the sorbet with an offset spatula, carefully covering the bottom of the crust. Drizzle 2 tablespoons of the rum mixture very slowly over the sorbet, allowing it to soak in. Repeat with the remaining sorbet and rum mixture. Smooth the top with the spatula. Loosely cover the pie with plastic wrap, and transfer to the freezer while preparing the whipped cream.
For the lime whipped cream: Beat the corn syrup, lime juice, rum and lime zest in a large bowl with an electric mixer on medium speed until combined. Add the heavy cream, and beat on medium-high speed until stiff peaks form. Remove the pie from the freezer, and quickly spread with the whipped cream, leaving a 1/2-inch border around the outside edge. Loosely cover the pie, and freeze until firm, at least 6 hours or overnight.
Garnish the frozen pie with 1/2 teaspoon of lime zest before serving.
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