Position a rack in the center of the oven and preheat to 350F. Spread the hazelnuts on a baking sheet and toast for 12 to 15 minutes, or until golden beneath the skins. Wrap the nuts in a clean towel and cool completely. Transfer the cooled hazelnuts to a large sieve and rub them back and forth to remove the loose skins. Make the chocolate butter cake: Position a rack in the center of the oven and preheat to 375F.
Line the bottom of a 17 1/2-by-11 1/2-inch jelly roll pan with parchment or waxed paper. Lightly spray the bottom and sides of the pan with nonstick cooking spray. In a medium bowl, whisk together the flour, cocoa powder, baking soda and salt. Sift the flour mixture onto a piece of waxed paper and set aside. In a 4 1/2-quart bowl of a heavy-duty electric mixer using the paddle attachment, beat the butter at medium-high speed for 1 minute, until creamy. While continuing to beat the butter, gradually add the granulated and brown sugars, stopping the machine and scraping down the side of the bowl as necessary. Beat the butter/sugar mixture at medium-high speed for 2 minutes, until smooth. Beat in the eggs, one at a time, and the vanilla.
Reduce the speed to low and alternately add one-third of the reserved dry ingredients and one-third of the coffee. In two more batches, alternately add the remaining dry ingredients and coffee, scraping down the bowl as necessary. Scrape the batter into the prepared pan and, using a metal cake spatula, smooth the batter evenly into the pan. Bake the cake for 25 to 28 minutes, until the sides just begin to pull away from the pan and the surface springs back when lightly touched. Cool the cake in the pan set on a wire rack for 10 minutes. Invert the cake onto a wire rack; carefully peel off the parchment paper and allow the cake to cool completely.
Make the caramelized hazelnuts and hazelnut praline: Lightly spray a baking sheet with nonstick cooking spray. In a small saucepan, combine the sugar and water. Cook over medium heat, stirring constantly, until the sugar dissolves. Increase the heat to medium-high and continue to cook without stirring for 4 to 6 minutes until the syrup caramelizes. Immediately remove the pan from the heat. Add the 12 perfect hazelnuts to the caramel and toss to coat. With an oiled fork, remove each hazelnut, letting the excess caramel drip back into the pan, and place them at one end of the prepared baking sheet. Quickly stir the 3/4 cup of hazelnuts into the remaining hot caramel. Pour the hazelnut praline onto the other end of the baking sheet. Cool the praline for 30 minutes until hard. Reserve the individual caramelized hazelnuts for decorating the cake. Coarsely chop the praline. In a food processor fitted with the metal chopping blade, process the praline for 35 to 45 seconds until finely ground. Transfer the praline to a bowl and set aside. Make the framboise syrup: In a small saucepan, combine the water and sugar. Cook over medium heat, stirring constantly with a wooden spoon until the sugar dissolves . Stop stirring; raise the heat to medium-high and bring the syrup to a boil. Remove the pan from the heat and stir in the framboise liqueur and vanilla.
Make the mascarpone cream filling: In a 4 1/2-quart bowl of a heavy-duty electric mixer using the wire whip attachment, beat together the mascarpone cheese, sugar and framboise liqueur at medium speed until combined, about 1 minute. While continuing to beat the mixture, gradually add the heavy cream; increase the speed to medium-high and beat the mascarpone mixture until soft peaks form and the mixture is spreadable. Cover and refrigerate the cream until ready to use. Assemble the cake: Using a long serrated knife, cut the cake lengthwise into 3 long strips of equal width. Place one cake strip on a wire rack. Using a pastry brush, moisten the top of the chocolate cake strip with some of the framboise syrup. Using an offset metal cake spatula, spread 1/4 cup of the mascarpone cream over the moistened cake strip. Cover the cream-coated strip with a layer of raspberries, placed stem-side-down in even rows over the cake (this will take approximately 2 1/3 cups of raspberries). Scrape l 1/2 cups of the mascarpone cream on top of the raspberries. Using a small offset metal spatula smooth the cream into an even layer, allowing it to settle into the gaps in between the raspberries. Sprinkle 1/4 cup of the ground praline over the cream layer. Place a second cake strip on top of the praline; repeat the preceding layering process and top with the final cake strip. Reserve the remaining ground praline to garnish the sides of the cake. Spread the remaining mascarpone cream in a thin even layer around the sides of the cake, filling in all the gaps. Place the wire rack with the cake on it in the refrigerator for l hour to set. Make the glaze: Place the chocolate in a medium bowl. In a small saucepan, bring the cream and corn syrup to a gentle boil. Pour the hot cream mixture over the chocolate.
Let the mixture stand for 30 seconds to melt the chocolate. Gently whisk until smooth. Allow the glaze to cool for 5 minutes. Glaze the cake: Remove the cake from the refrigerator and place the wire rack on a baking sheet. Pour the glaze over the cake, covering it completely. While the glaze is still wet, put the remaining ground praline around the sides of the cake. Refrigerate the cake for 5 to 10 minutes, until the glaze is set. Garnish the top of the cake with the caramelized hazelnuts.