Make the chestnut puree: In a small food processor, pulse to combine the chestnuts and 2 tablespoons sugar. With the machine running, add 1 tablespoon of rum and process for about 2 minutes, or until the puree is no longer grainy, stopping every 30 seconds to scrape down the sides. Alternatively, use a mortar and pestle to grind the chestnuts and sugar together, then add the rum and grind into a smooth puree.
Make the filling: Place a medium metal bowl in the freezer. In a medium pot, whisk together ½ cup sugar, the gelatin, and the salt. Whisk in the egg yolks, followed by the chestnut puree, then gradually whisk in the cream, followed by the milk. Cook over medium heat, stirring constantly and scraping the bottom of the pan with a silicone spatula, until the mixture thickens just enough to coat the spatula and reaches 180°F on a candy thermometer, 10–15 minutes. Remove from the heat and immediately pour the mixture into the chilled bowl. Stir in the remaining 3 tablespoons of rum and refrigerate, stirring every 10 minutes, until the custard is chilled and thickened, about 1 hour.
Once the custard is cold, make the meringue: In a small pot, combine the remaining ⅔ cup sugar with 3 tablespoons of water. Cook over medium heat, stirring with a silicone spatula until the sugar has dissolved and the syrup begins to bubble, about 5 minutes. Turn off the heat.
Meanwhile, in the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites on medium-high speed until soft peaks form. With the mixer running, pour the hot sugar syrup in a thin stream into the foamy egg whites. Add the vanilla and continue beating until the meringue holds medium-stiff peaks but is still silky, not foamy, 3–5 minutes. Transfer about ¾ of the meringue from the mixer into a clean bowl and set aside, leaving the remainder on the whisk attachment or in the mixer bowl. Pour the chestnut custard into the mixer bowl and beat with the residual meringue until very smooth and lightened. Remove the bowl from the mixer, then fold in the reserved meringue just until combined.
Assemble the pies: Pile a heaping cup of filling into each of the pie shells, using a spatula to spread it around the bottoms. Gently fold about two-thirds of the macerated cherries into the remaining filling and divide it between the two pie shells, making sure to scrape the entire contents from the sides of the bowl into the pies, spreading the filling to the edges of the crusts, and mounding it slightly in the centers. Refrigerate the pies until set, about 4 hours.
Meanwhile, in a medium bowl, whisk together the remaining heavy cream with the confectioner’s sugar, the remaining vanilla extract, and the salt. Beat until the cream is voluminous and holds its shape but is still very smooth. If topping the pies with chocolate shavings, sprinkle the surfaces of the pies with them, then dollop each pie with whipped cream and the remaining cherries. If topping with ganache, transfer the warm ganache to a pastry bag fitted with a narrow tip and pipe it over the pies in a crisscross pattern. Transfer the whipped cream to another pastry bag fitted with a round tip and pipe the whipped cream around the edge of each pie. Top with the remaining cherries. To serve, slice with a hot, wet knife to avoid dragging the chiffon. Nesselrode pie is best enjoyed right away, but it will keep for up to 2 days, covered, in the fridge.