Method
To make the chestnut cream: The day before you want to serve the tart, in a saucepan over medium heat, combine the heavy cream and mascarpone and warm, stirring frequently, until just below the boiling point.
In a bowl, whisk together the egg yolks and granulated sugar. When the cream mixture is just about to boil, remove the saucepan from the heat and, whisking constantly, slowly add 1⁄2 cup (120ml) of the hot liquid to the yolk-sugar mixture, until smooth.
Return the egg-cream mixture to the saucepan over medium heat and cook, whisking nonstop, until the custard begins to thicken, four to five minutes. Remove from the heat and whisk in the chestnut purée.
Submerge the gelatin sheets in a bowl of cold water for 10 minutes. Squeeze the excess water from the softened gelatin and whisk the gelatin into the chestnut mixture.
Let cool to room temperature—stirring from time to time to stop a skin from forming, or laying plastic wrap directly on the surface. Refrigerate overnight.
To make the meringue caps: Preheat the oven to 200°F (95°C). Line a baking sheet with parchment paper, then mark the paper with 12 two-inch (five cm) circles, using a ring mould as your guide.
Using a stand mixer fitted with the whisk attachment, at medium-low speed, beat the egg whites until foamy. Add the salt, increase the speed to medium, and continue to whip until the egg whites form soft peaks—they should have the consistency of shaving cream.
Add the granulated sugar one-third at a time and then beat at medium speed for one minute more. Increase the speed to medium-high, whisking until long stiff peaks form when you lift the whisk.
Transfer this meringue to a pastry bag fitted with a 1⁄6-inch (four mm) plain tip and pipe as many two-inch (five cm) rounds as you can onto the prepared baking sheet—once cooked, you’ll be picking the nicest six meringues.
Bake until meringue is firm to the touch, for one-and-a-half to two hours (if the meringues start to colour during baking, lower the heat). Transfer the meringues to a rack and let cool completely.
To make the pastry shells: Sift the flour, confectioners’ sugar, and salt into a large bowl. Add the vanilla bean seeds. Add the butter and rub the mixture in with your fingertips until it resembles fine bread crumbs.
Add the egg yolk and, using a spatula, stir it into the mixture until a firm dough forms (you may need to add a splash of cold water if the dough feels crumbly). Knead the dough briefly and gently on a floured surface. Wrap in plastic and refrigerate for 30 minutes.
Preheat the oven to 325°F (160°C). Line a baking sheet with parchment paper.
On a lightly floured work surface, roll out the dough to a thickness of 1⁄8 inch (three mm). Using a sharp knife or a pizza wheel and a ruler, cut six strips each measuring about 3⁄4 by 81⁄2 inches (two by 21cm).
Arrange each strip around the inside of the perforated tart rings, applying gentle pressure where the dough overlaps to secure the seal. Place each lined ring onto the prepared baking sheet.