Preheat oven to 300F and butter three 9-inch round cake pans. Line the bottoms with rounds of parchment and butter the paper.
Finely chop the chocolate and place in a medium-sized nonreactive bowl. Pour the hot coffee over the chocolate and let the mixture stand, stirring occasionally, until the chocolate is melted and the mixture is smooth.
In a large bowl sift together sugar, flour, cocoa powder, baking soda, baking powder, and salt. In another large bowl with an electric mixer beat eggs until thickened slightly and lemon colored (about 3 minutes with a standing mixer or 5 minutes with a hand-held mixer). Slowly add the oil, buttermilk, vanilla, and melted chocolate mixture to eggs, beating until combined well. Add the sugar mixture and beat on medium speed until just combined well.
Divide batter between pans and bake in middle of oven until a tester inserted in center comes out clean, 35-45 minutes.
Cool the layers completely in pans on racks. Run a thin knife around edges of pans and invert layers onto racks. Carefully remove parchment paper and cool the layers completely. Cake layers may be made 1 day ahead and kept, wrapped well in plastic wrap, at room temperature, or can be frozen for several days.
Make Raspberry Filling
Puree the raspberries in a food processor, blender or immersion blender. Press the puree through a fine-mesh strainer with the back of a spoon, removing the seeds. Heat the puree in a small pot with the sugar and cornstarch until mixture boils, stirring constantly. As it boils, it should thicken quickly. Let it thicken to about the consistency of cold maple syrup.
Let it cool complete before spreading it over two layers.
Finely chop the chocolate. In a 1 1/2- to 2-quart saucepan bring cream, sugar, and corn syrup to a boil over moderately low heat, whisking until sugar is dissolved. Remove pan from heat and add chocolate, whisking until chocolate is melted. Cut butter into pieces and add to frosting, whisking until smooth.
Transfer the frosting to a bowl and cool, stirring occasionally, until spreadable (depending on chocolate used, it may be necessary to chill frosting to spreadable consistency). If necessary, you can stir the ganache over a bowl of ice water to cool it off quickly and evenly.
Spread frosting over the top and sides of the cake. The cake keeps, covered and chilled, 3 days. Bring cake to room temperature before serving.
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