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Grease and flour 2 nine inch round cake pans and line the bottom with 2 circles of parchment paper. Sift together both flours, baking soda. baking powder, salt and sugar, Set aside.
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In the bowl of an electric mixer beat together the vegetable oil, shortening and vanilla extract. Beat well at high speed with whisk attachment until light and fluffy
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Beat the eggs in one at a time.
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Fold in the lime zest.
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Fold in the dry ingredients alternately with the buttermilk.
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I always add dry ingredients in three divisions and liquid ingredients in 2 divisions. It is very important to begin and end the additions with the dry ingredients. Do not over mix the batter. As soon as it has no lumps in the batter, pour into the two prepared 9 inch cake pans.
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Bake at 325 degrees F for 30-35 minutes or until a wooden toothpick inserted in the center comes out clean. Allow the cake to cool in the pans for 10 minutes before turning out onto wire racks to cool completely.
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FOR THE FROSTING: mix together the icing sugar, lime zest and butter until it becomes sort of crumbly.
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Add the lime juice and a little of the milk.
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Beat until smooth and fluffy, adding only enough milk to bring the frosting to a creamy spreadable consistency.
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Fill and frost the cake. Garnish with candied llime zest if desired.
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To make candied lime zest, remove the zest with a sharp vegetable peeler in long strips, avoiding as much of the white pith as possible.
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Bring one cup of water and one cup of sugar to a slow boil.
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Add the pieces of lime zest and boil for about 15 minutes. Drain the lime zest on a wire rack.
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When cool, cut them in strips and roll in fine sugar.