How to Make It
Place the hazelnuts in a food processor, add 1 tablespoon of the sugar and process until fine. Scrape the nuts into the bowl of a standing mixer fitted with the paddle. Add the flour, salt and the remaining 3 tablespoons of sugar and mix until combined. Add the butter and mix at low speed until incorporated. Add the egg and vanilla and mix until a soft dough forms. Scrape the pastry onto a sheet of plastic wrap and flatten into a disk. Wrap and refrigerate for 1 hour.
Preheat the oven to 350° and coat a 9-inch fluted tart pan with a removable bottom with vegetable oil spray. Roll out the pastry between 2 sheets of wax paper to a 12-inch round. Ease the pastry into the tart pan, pressing it into the corners and patching any tears. Roll the rolling pin over the tart pan to cut off any excess pastry. Refrigerate the tart shell for 10 minutes.
Line the pastry with parchment paper and fill it with pie weights or dried beans. Bake in the center of the oven for 20 minutes. Carefully remove the parchment and weights and bake the shell for about 15 minutes longer, until golden brown. Let cool completely.
Put the chocolate in a heatproof bowl. In a small saucepan, bring the cream just to a simmer. Pour the hot cream over the chocolate and let stand for 5 minutes; whisk until smooth. Pour the chocolate cream into the tart shell and scatter the hazelnuts on top. Refrigerate until firm, about 1 hour and 30 minutes. Remove the tart ring, cut the tart into wedges and serve.
To toast and skin hazelnuts, preheat the oven to 350 degrees. Spread the hazelnuts in a pie plate and toast for about 12 minutes, until golden and the skins blister. Let cool slightly, then transfer the hazelnuts to a kitchen towel and rub off the skins. Let cool.