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Preheat the oven to 350°F. Lightly grease two 9" x 2" round cake pans: one for the vanilla cake, one for the chocolate. If desired, line with parchment, and grease the parchment; this will ensure the cakes turn out intact.
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To make the vanilla cake: Beat the eggs and sugar until smooth. Gradually add the vegetable oil, beating all the while. Stir in the salt, baking powder, and vanilla
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Gently mix in the flour in three parts, alternating with the cream and starting and ending with the flour.
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Pour the batter into one of the prepared pans.
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Bake the cake for 30 to 35 minutes, until the cake is beginning to brown on top. It may crack slightly; that's OK.
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Remove the cake from the oven, and after 10 minutes turn it out of the pan onto a rack to cool.
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To make the chocolate cake: Whisk together the dry ingredients.
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Add the eggs, oil, and vanilla, beating until smooth.
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Gradually add the water, beating until smooth.
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Pour the batter into the prepared pan.
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Bake the cake for about 35 minutes, or until a cake tester inserted into the center comes out clean.
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Remove the cake from the oven, and after 10 minutes turn it out of the pan onto a rack to cool.
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Divide the cooled cakes in half horizontally, to make four round layers. Place one vanilla layer on a serving plate.
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To make the filling: Beat the butter and salt until smooth. Add the confectioners' sugar, vanilla extract, and 2 tablespoons of the milk, and beat until fluffy. Add additional milk if the frosting seems too stiff to spread.
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Spread 1/3 of the filling on the cake, spreading to within about 1/2" of the edge.
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Top with a chocolate layer. Spread with 1/3 of the filling.
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Top with the second vanilla layer. Spread with the remaining filling.
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Top with the second chocolate layer.
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To make the icing: Combine the chocolate and cream in a microwave-safe bowl, and heat until the cream is very hot, and the chocolate very soft.
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Stir to melt the chocolate completely, reheating very briefly if necessary.
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Pour and spread the icing over the top of the cake, letting it drip over the edges and down the sides. Once it's done dripping, smooth the sides with a spatula.
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Add sugar decorations while the icing is still warm.
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Allow the cake to rest, covered with a cake cover (or a big turned-over bowl) until the chocolate is set; overnight is good, though several hours are sufficient.