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1
Ganache: Place chocolate in medium bowl. Bring cream, lime leaves, zest and lime juice to a bare simmer over moderately low heat. Remove from heat and let steep, covered, 25 min. Return cream mixture to a simmer. Pour hot cream over chocolate; cover with plastic wrap and let stand 15 min. Whisk cream and chocolate until smooth. Mix flaked coconut and corn syrup in small bowl to coat; stir into chocolate mixture. Let cool to lukewarm. Stir in butter. Cover and let stand at room temperature overnight to set.
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2
Syrup: Place 1/2 cup water, sugar, and rum in small saucepan. Stir over medium heat until sugar dissolves. Simmer 1 minute; remove from heat.
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3
Cake: Preheat oven to 350u00b0F. Butter and flour three 8-inch cake pans. Line with parchment.
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4
Whisk 2 cups boiling water, cocoa powder, and 1/2 cup coconut in medium bowl. Whisk flour, baking soda, baking powder, and salt in large bowl. Using electric mixer, beat sugar and butter with mixer in large bowl until fluffy, about 1 min. Add eggs 1 at a time, beating until incorporated after each addition. Beat in vanilla extract. Add flour mixture in 4 additions alternately with cocoa mixture in 3 additions. Divide batter among cake pans. Bake cakes until tester inserted into center comes out clean, about 30 minutes. Cool in pans 5 min. Turn out onto racks; cool completely.
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5
Whipped cream frosting: Beat cream in large bowl until soft peaks form. Add sugar, vanilla, lime zest, and lime juice. Beat until stiff peaks form.
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6
Trim rounded tops off cakes with a serrated knife. Place 1 cake layer, cut side up, on plate. Brush top with 1/3 cup rum syrup. Spread half of ganache over top of cake. Place second layer, cut side up, atop first layer. Brush with 1/3 cup syrup; spread with remaining ganache. Top with third cake layer. Brush with remaining syrup. Spread sides and top with whipped cream frosting. Sprinkle top with coconut. Refrigerate about 4 hrs to set ganache. Let stand at room temperature 30 minutes before serving.
