Make the pastry In a food processor, pulse the 3 cups of flour, the confectioners’ sugar, salt and vanilla seeds until combined. Add the butter and pulse until the mixture resembles coarse meal. Drizzle in the cream and pulse just until a dough starts to form. Scrape onto a lightly floured work surface, gather up any crumbs and knead gently just until the dough comes together. Pat into 2 equal disks, wrap in plastic and refrigerate until firm, about 1 hour.
Between 2 sheets of plastic wrap, roll out 1 piece of dough to a 14-inch square, about 1/8 inch thick. Using a knife, cut out three 7-inch rounds. Ease each round into a 4-inch tart pan with a removable bottom, then trim the overhang and prick the dough all over with a fork. Repeat with the remaining piece of dough. Freeze until firm, about 15 minutes.
Preheat the oven to 350°. Line the tart shells with parchment paper and fill with pie weights or dried beans. Set the shells on a large rimmed baking sheet. Bake for 20 minutes, until the edges are lightly golden. Remove the paper and weights and bake for 15 to 20 minutes longer, until the shells are golden. Transfer to a rack and let cool completely.
Meanwhile, make the caramel In a medium saucepan, gently stir the superfine sugar with the water. Using a wet pastry brush, wash down the side of the saucepan to remove any sugar crystals. Cook over moderately high heat until a medium-amber caramel forms, about 8 minutes. Remove from the heat and slowly add the cream (the mixture will bubble vigorously). Return to the heat and cook for 1 minute, stirring the caramel until smooth. Transfer to a bowl and let cool, then cover and refrigerate until cold and firm, about 2 hours.
Make the filling Put the chocolate in a heatproof medium bowl and set it over a saucepan of barely simmering water. Melt the chocolate, stirring occasionally, until smooth. Remove from the heat and let cool. In the bowl of a stand mixer fitted with the whisk, beat the egg whites with a pinch of salt at medium-high speed until stiff peaks form, about 2 minutes. Fold one-third of the beaten whites into the cooled chocolate to lighten it, then fold in the remaining whites until combined. In a clean bowl, beat the heavy cream to soft peaks. Gently fold the chocolate mixture into the whipped cream until combined. Spoon the chocolate cream into the pastry shells and smooth the tops. Chill until firm, about 1 hour.
Preheat the oven to 350°. Just before serving, remove the tarts from the pans and arrange on a baking sheet. Heat for 2 to 3 minutes, until the chocolate begins to melt and the tops appear shiny. Dust the tarts liberally with cocoa powder, then transfer to plates. Put a spoonful of crème fraîche on each plate and sprinkle with turbinado sugar. Scoop some caramel alongside and serve.
The finished tarts (without the cocoa) can be refrigerated overnight. Bring to room temperature for 30 minutes before heating. The caramel can be refrigerated for up to 1 week.
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