1Preheat oven to 300°F. You will need two 10x2-inch round cake pans. Line bottoms with rounds of wax paper and grease paper.
2Finely chop chocolate and combine in a bowl with hot coffee. Let mixture stand, stirring occasionally, until chocolate is melted and mixture is smooth.
3Into a large bowl sift together sugar, lour, cocoa powder, baking soda, baking powder, and salt.
4In 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).
5Slowly add oil, buttermilk, vanilla, and melted chocolate mixture to eggs, beating until combined well. Add sugar mixture and beat on medium speed until just combined well.
6Divide batter between pans and bake in middle of oven until a tester inserted in center comes out clean, 1 hour to 1 hour and 10 minutes.
7Cool layers completely in pans on a rack, then invert layers onto racks. Carefully remove wax paper.
8MAKING FROSTING: Finely chop 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. Cool until spreadable (you may need to chill frosting a bit).
9Spread frosting between cake layers and over top and sides. Cake will keep if covered and chilled. Bring to room temperature before serving.