- Preheat an oven to 375°F. Lightly butter and flour a 9-inch round springform cake pan.
- To make the torte, spread the 1/2 cup hazelnuts on a baking sheet and toast in the oven until lightly browned and fragrant, 5 to 7 minutes. While the nuts are still warm, place them in a kitchen towel and rub with the towel to remove the skins. Do not worry if bits of skin remain. Set aside.
- Place the chocolate and butter in a large heatproof bowl set over but not touching gently simmering water in a saucepan. Stir often until the chocolate melts, then remove from the heat.
- In a food processor fitted with the metal blade or in a blender, combine the skinned nuts with the 2/3 cup sugar. Pulse until finely ground. Add to the chocolate mixture and stir until blended. Let cool; then add the egg yolks one at a time, beating well after each addition. In a bowl, sift together the flour and cocoa. Stir into the chocolate mixture.
- In another bowl, using an electric mixer, beat the egg whites and cream of tartar until soft peaks form. Add the 2 tablespoons sugar and beat until stiff peaks form. Using a rubber spatula, fold one-fourth of the whites into the chocolate mixture to lighten it. Then fold in the remaining whites just until no white streaks remain. Pour into the prepared pan.
- Bake until a skewer inserted into the center comes out almost clean, 35 to 40 minutes. Transfer the pan to a wire rack and let cool.
- To make the glaze, combine the chocolate, butter and corn syrup in a heatproof bowl set over but not touching gently simmering water in a saucepan. Stir often until the chocolate melts, then remove from the heat and stir until smooth. Let cool, stirring occasionally, for 15 minutes; the glaze will thicken slightly.
- Set the rack over a baking sheet, invert the torte onto the rack and lift off the pan. Pour on the glaze, tilting the torte to coat the top and sides completely. When the glaze stops dripping, place the 12 hazelnuts around the top of the cake. Transfer to a serving plate and serve. Makes one 9-inch torte.