Make the crust: Preheat the oven to 350 degrees F. Toast the fennel seeds in a small dry skillet over medium heat until fragrant, about 2 minutes. Pulse the cookies in a food processor until finely ground. Add the fennel seeds and melted butter; pulse until moistened. Press the mixture evenly into the bottom and up the side of a 9-inch pie plate. Bake until lightly browned and set, about 8 minutes; let cool completely.
Make the filling: Combine the chestnuts, sugar, 1 cup heavy cream and the vanilla seeds and pod in a medium saucepan. Bring to a boil, then reduce the heat to low and simmer, stirring occasionally, until the cream is very thick and the chestnuts are softened, 25 to 30 minutes.
Meanwhile, melt the butter in a small saucepan over medium heat; cook until it smells nutty and is golden brown, about 4 minutes. Discard the vanilla pod from the chestnut mixture; transfer the mixture to a food processor, add the browned butter and process until smooth. With the machine running, slowly add the remaining 1½ cups heavy cream and the eggs; process until combined. Let stand until thickened and cooled, about 1 hour.
Carefully pour the filling into the crust (it will be full). Bake at 350 degrees F until the filling is set, about 45 minutes. Transfer to a rack and let cool completely.
Make the meringue: Bring a few inches of water to a boil in a large saucepan. Whisk the sugar, cream of tartar, salt and egg whites in the bowl of a stand mixer. Set the bowl over the boiling water (don't let the bowl touch the water); continue whisking until the mixture is hot (135 degrees F) and the sugar dissolves, 2 to 3 minutes.
Transfer the bowl to the stand mixer; beat with the whisk attachment on medium-high speed until soft peaks form, about 2 minutes. Increase the speed to high and beat until stiff, thick and glossy, 2 to 3 more minutes. Spread the meringue on top of the pie. Toast with a kitchen torch.