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Make the cake:Onto a sheet of wax paper sift the flour 3 times.
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In a large bowl with an
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electric mixer beat the egg whites with the salt till they are frothy, add in the cream of tartar, and beat the whites till they hold soft peaks.
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Beat in 1/2 c. of the sugar, a little at a time, add in the vanilla and the almond extract, and beat the whites till they hold stiff peaks.
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Mix in the remaining 1/2 c. sugar, a little at a time, sift the flour over the whites in 4 batches, folding it in gently after each addition, and mix in
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the coconut.
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Spoon the batter into a tube pan, 9 inches across the top and 3 1/2 inches deep, and bake the cake in the middle of a preheated 275F.
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oven for 1 1/2 hrs.
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Hang the cake in the pan upside down on the neck of a bottle and let it cold for 1 1/2 to 2 hrs, or possibly till it is cooled completely.
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Release the cake from the side of the pan and from the
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center tube with a sharp knife, turn it out onto a rack, and invert it onto a cake plate.
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Make the frosting:In a metal bowl whisk together the sugar, the egg whites, the zest, the orange juice, the corn syrup, and healthy pinch of salt, set the bowl over a saucepan of simmering water, and cook the mix, whisking till it registers 140F.
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on a candy thermometer.
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Remove the pan from the heat and whisk the mix over the warm water for 3 min.
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Remove the bowl from the pan and with an electric mixer beat the frosting at high speed for 7 to 10 min, or possibly till it is cold and hold stiff peaks.
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Spread the top and sides (including the center) of the cake with the frosting and coat the outside with the toasted coconut.