Step 1

In a food processor, pulse the confectioners' sugar with the butter and vanilla seeds until smooth. Add the egg yolk and water and process until blended. Add the flour and salt and pulse until the pastry just comes together. Pat the pastry into a disk, wrap in plastic and refrigerate until just firm enough to roll out, about 20 minutes.

Step 2

Preheat the oven to 350°. Roll out the dough between 2 sheets of plastic wrap to an 11-inch round. Peel off the top sheet of plastic and invert the dough over a 9-inch fluted tart pan with a removable bottom. Discard the plastic and fit the pastry into the pan. Trim the overhang to 1/2 inch, fold in to reinforce the sides, and patch any holes. Prick the bottom of the tart shell with a fork and refrigerate until chilled, about 30 minutes.

Step 3

Line the pastry shell with foil and fill with pie weights or dried beans. Bake for 25 minutes, or until the pastry is set and the edges are golden. Carefully remove the foil and weights. Cover the rim of the tart with foil strips and bake for about 5 minutes, or until the pastry is golden and cooked through. Transfer to a rack and let cool.

Step 4

In a small saucepan, warm 1/4 cup of the cream with the vanilla seeds and baking soda. In a medium saucepan, cook 1/2 cup of the sugar with the corn syrup over moderate heat until a deep amber caramel forms, about 8 minutes. Remove the pan from the heat and stir in 4 tablespoons of the butter. Slowly stir in the vanilla cream in a thin stream. Cook the caramel over moderate heat until slightly thickened, about 3 minutes. Pour the hot caramel into the pastry shell and refrigerate until set, about 30 minutes.

Step 5

In another medium saucepan, simmer the remaining 1/2 cup of sugar with the water over high heat, stirring just until the sugar dissolves, about 2 minutes. Add the hazelnuts and cook over moderate heat, stirring frequently, until toasted and caramelized, about 10 minutes. The sugar will get very hard and crystallized after about 5 minutes, then it will melt and caramelize and the nuts will toast. Reduce the heat if the caramel darkens before the nuts are toasted. Stir in the remaining 1 tablespoon of butter. Pour the caramelized nuts onto a sheet of parchment paper and let cool completely. Transfer the nuts to a plastic bag and crush lightly with a rolling pin.

Step 6

In a small saucepan, heat the remaining 3/4 cup of cream until bubbles appear around the edge. Remove from the heat, add the chocolate and let stand until melted, about 5 minutes. Whisk the chocolate until smooth, then pour it over the caramel in the tart shell. Jiggle the pan to spread the chocolate in a smooth layer. Sprinkle the crushed, caramelized hazelnuts on top and refrigerate until set, about 15 minutes.

Step 7

Remove the tart pan and transfer the tart to a serving plate. Cut the tart into wedges and serve with whipped cream.