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Preheat the oven to 350°F. Grease a half-sheet pan (13" x 18"), line it with parchment, and grease the parchment.
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To make the cake: Combine the chocolate, butter, oil, water, and cocoa in a medium saucepan or microwave-safe bowl.
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Heat, stirring occasionally, until the mixture is smooth. Transfer it to a mixing bowl.
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In a separate bowl, mix together the flour, sugar, baking soda, and salt until evenly combined.
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Add the dry ingredients to the chocolate mixture, stirring until just combined.
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Mix together the buttermilk, eggs, yolks, and vanilla, then add to the other ingredients, again mixing until just combined.
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Pour the batter into the prepared pan, spreading it into an even layer.
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Bake the cake for 18 to 20 minutes, until a cake tester inserted into the center comes out clean. Remove it from the oven, and allow it to cool completely in the pan.
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To make the icing: Combine the chocolate, corn syrup, vanilla, and heavy cream in a microwave-safe bowl.
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Microwave until the cream is very hot, and the chips have softened. Stir until the chips have melted and the mixture is smooth, reheating briefly if necessary.
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Add the confectioners' sugar and cocoa, and beat until smooth.
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Spread the icing evenly onto the cooled cake, and allow it to set for 30 to 60 minutes before serving.