An edible masterpiece of chocolate, with a subtle orange flavor, this cake is the perfect finale to a very special dinner. Layers of dark chocolate cake alternate with whipped ganache, then it is coated with a shiny glaze.
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To make the orange syrup, stir the simple syrup and liqueur together.
To make the whipped ganache, bring 3/4 cup plus 2 tablespoons of the cream to a simmer in a medium saucepan over medium heat. Put the chocolate in a heatproof bowl. Add the hot cream and let stand until the chocolate softens, about 3 minutes. Whisk until smooth. Let cool until tepid but still fluid, about 15 minutes.
Whip the remaining 1 1/4 cups plus 2 tablespoons cream in the chilled bowl of a heavy-duty stand mixer fitted with the whisk attachment on medium speed only until the cream holds its shape, just before soft peaks begin to form. Pour the whipped cream over the cooled chocolate mixture and fold together with a silicone spatula. Do not overmix, or the ganache will be grainy. Transfer 1/2 cup of the ganache to a small bowl and set aside.
To assemble the cake, transfer the cake, with its cutting board, to the work surface. Using an 8 by 3-inch metal cake ring as a template, cut out two 8-inch rounds of cake from opposite corners of the chocolate cake. Cut out two half-rounds of cake from the remaining cake, and save the scraps. The two half-rounds will be put together, with the reserved scraps cut to fill in the gap, to become the center cake layer.
Place the cake ring on a half-sheet pan. Insert an 8-inch cardboard round, white side up, inside the ring. Place a whole cake layer in the ring, and drizzle and brush with about 3 1/2 tablespoons of the syrup. Top with half of the whipped ganache filling, and spread evenly. Top with the partial cake layers, and fill in the gap with trimmings of the reserved cake scraps. Top with a smaller cardboard round and press gently to level the layers. Remove the cardboard round. Drizzle and brush the layer with another 3 1/2 tablespoons syrup. Spread with the rest of the filling. Add the final cake layer, cover with the smaller cardboard round, and press gently to level the layers. Remove the cardboard round. Drizzle and brush the cake with the remaining syrup. Using a small offset spatula, spread the reserved 1/2 cup filling over the top cake layer to make a smooth surface that fills any small holes. Refrigerate the cake until completely chilled, at least 6 hours or overnight.
Remove the cake from the refrigerator. Place on the work surface. Rinse a kitchen towel under hot water and wring it out. Wrap the hot, moist towel around the sides of the cake ring, being careful not to get water on the top of the cake. Let stand for about 30 seconds. Lift up on the ring to remove it. (If it doesn't remove easily, moisten the towel again and reapply to the sides.) Place the cake on a small round wire cake rack set on a half-sheet pan. Using a small offset spatula rinsed under hot water and dried, smooth the sides of the cake to even out the exposed ganache between the layers. Refrigerate the cake on the rack until the outer layer of ganache is very firm, about 30 minutes.