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1.
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To make the buttercream: Stir the sugar and water in a small saucepan over low heat until the sugar dissolves, about 5 minutes.
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Increase the heat to medium and boil, without stirring, until the syrup reaches the soft-ball stage, or 250F on a candy thermometer, about 10 minutes.
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2.
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Meanwhile, beat the egg yolks until pale and thick, about 4 minutes.
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In a slow, steady stream, pour the hot syrup into the eggs, beating continuously as you pour.
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(Do not let the syrup touch the beaters or it will spin into threads.)
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Continue beating until the mixture thickens and cools to room temperature, about 10 minutes.
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3.
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Beat in the butter and shortening, 2 tablespoons at a time, until absorbed.
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Gradually beat in the chocolate.
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Blend in the vanilla, salt, and rum if using.
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Do not add the flavoring too quickly or the buttercream might curdle.
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Chill until of spreading consistency, at least 2 hours or up to 1 week.
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If the buttercream firms too much, return to room temperature before using, about 1 hour.
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4.
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Preheat the oven to 350F.
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Grease the bottoms of several 9-inch round cake pans and dust with flour, tapping out the excess.
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Or grease and flour several large baking sheets and, using a 9-inch saucepan lid or springform pan, mark 9-inch circles on the sheets.
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5.
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To make the batter: Beat the eggs and sugar until thick and creamy, 5 to 10 minutes.
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Add the vanilla and salt.
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Sift the flour over the top and carefully fold it in.
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6.
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Spread about 1/4 cup of the batter evenly over the bottom of the prepared pans or over each circle on the baking sheets.
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7.
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Bake until the edges begin to color, 5 to 7 minutes.
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Loosen with a spatula, invert onto a rack, and let cool.
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Wipe the pans, regrease, dust with flour, and repeat until there are 7 or 8 matching layers.
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8.
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To make the caramel if using: Stir all the caramel ingredients in a small saucepan over low heat until the sugar dissolves, about 5 minutes.
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Stop stirring, increase the heat to medium, and cook, swirling the pan occasionally, until the syrup turns a deep amber color.
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Do not burn.
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9.
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Using a lightly oiled metal spatula, spread all of the caramel evenly over one of the cake layers.
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Let set slightly (do not let it harden), then use an oiled knife to cut just the caramel into 8 to 10 wedges (indicating where the cake will be sliced).
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10.To assemble: Place a cake layer on a serving plate, spread with 1/8-inch thick layer of buttercream, then place a second layer on top.
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Repeat layering the buttercream and cake layers.
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Cover the top of the cake with buttercream.
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If using the caramel layer, place on top of the cake.
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Cover the sides of the cake with buttercream.
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Chill.
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Store in the refrigerator for up to 1 day or in the freezer.
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Let stand at room temperature for at least 30 minutes before serving.
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Oblong Layer Cake: Divide the batter between two 15 1/2-by-10 1/2-inch jelly roll pans and bake.
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After cooling the cakes, cut each lengthwise into 3 equal pieces to make a 6-layer cake.