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1
Place egg whites in a large bowl; let stand at room temperature for 30 minutes.
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2
Meanwhile, place ginger and 2 tablespoons sugar in a small food processor; cover and process until finely chopped.
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3
In a large bowl, combine the flour, 1-1/4 cups sugar, baking powder, salt and ginger mixture. In another bowl, whisk the egg yolks, eggs, oil, water and extract. Add to dry ingredients; beat until well blended.
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4
Add cream of tartar and remaining sugar to egg whites; beat with clean beaters until stiff peaks form. Fold into batter.
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5
Gently spoon into three ungreased 9-in. round baking pans. Cut through batter with a knife to remove air pockets. Bake on the lowest oven rack at 325u00b0 for 22-26 minutes or until cake springs back when lightly touched.
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6
Cool for 10 minutes before removing from pans to wire racks to cool completely.
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7
In a large bowl, beat butter until fluffy. Add the confectioners' sugar, milk, extract and salt; beat until smooth.
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8
Place bottom cake layer on a serving plate; spread with 1 cup frosting. Repeat layers twice. Frost sides of cake with remaining frosting. Press coconut over top and sides of cake. Garnish with orange and lime peel if desired. Refrigerate until serving.
