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Preheat oven to 350 degrees Fahrenheit or 175 degrees Celsius. Grease and dust two 9*2 inch cake pans with flour. Whisk together flour + baking soda + baking powder + salt and keep aside.
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In a large bowl beat butter + sugar until fluffy. Add oil and beat well. Now add one yolk at a time beating well after each addition. Stir in vanilla extract. Add flour in three batches alternating with coconut milk beginning and ending with flour. Fold in the coconut.
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Beat egg whites in a clean bowl until soft peaks form. Yield better results if the egg is at room temperature. Carefully fold in the egg whites taking care not to over mix.
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Pour into two 9 * 2 inch round pans.
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Bake for 25-35 minutes or until the tooth pick inserted in the center of the cake comes out clean.
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Let the cake stand for 10 minutes and then carefully transfer onto a wire rack for cooling.
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Icing:
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Beat the butter, cream cheese and milk until fluffy. Gradually add the confectioners sugar and beat well until soft. Increase or decrease the sugar as needed. (I cannot stop tasting the icing when I am making )
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To start the icing let the cake cool completely. Place one cake on the cake stand. Spread the frosting in the center of the cake leaving 1 inch around the edges. Place another cake on top. Top it with icing and spread evenly on the top and towards the sides. Sprinkle shredded coconut generously all over the cake.