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Preheat oven to 350F. Generously coat 3 (9 inch) round cake pans with coconut oil and flour the pan, discarding excess.
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Place shredded coconut in bowl of food processor and pulse until very finely chopped.
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In large mixing bowl, combine the chopped coconut, flour, baking powder, and salt.
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In a separate bowl, whisk the coconut milk, cream of coconut, egg whites, vanilla and lemon zest until completely blended.
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In bowl of stand mixer with paddle attachment, cream the sugar and coconut oil on high speed until light and fluffy. Reduce speed to medium low and beat in the 3 whole eggs, one at a time, until well combined. Add the flour mixture, alternating with the coconut milk mixture, to the creamed oil and sugar mixture, starting and ending with the flour.
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Divide batter equally in the 3 prepared pans. Bake for about 35 minutes or until the layers are light golden and set (you can check with a toothpick to make sure it comes out clean). Cool in pan for 15 minutes, then remove to wire racks and cool completely prior to assembly.