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- Preheat oven to 350°F. Mist 3 8-inch round cake pans with cooking spray.
- Prepare cake: In a medium bowl, whisk together flour, shredded coconut, baking powder and salt; set aside. In a separate medium bowl, place egg whites; using an electric hand mixer, beat on medium-high until stiff peaks form, about 5 minutes. Set aside.
- In a large bowl, place sugar and coconut oil. Beat on medium-high until creamy, 2 minutes; add yolks, coconut milk, vanilla and coconut extracts, mixing to combine. Scrape down sides of bowl; beat for 1 more minute. Turn speed to low and add flour mixture in 3 batches. When flour is fully incorporated, fold inone-third of egg whites and repeat until all of whites are incorporated.
- Divide batter among prepared pans. Bake until a toothpick inserted in middle comes out clean, 25 minutes. Set aside to cool in pans, 15 minutes. Invert onto a wire rack; cool completely.
- Meanwhile, prepare icing: Place 2 inches water in a medium saucepan and bring to a simmer. In a medium heat-proof bowl, whip egg whites and sugar with a whisk until well combined. Set bowl over simmering water, making sure bottom does not touch water. Cook, beating on medium-high with electric hand mixer, until mixture is hot (160°F) and no longer grainy, 5 to 6 minutes.
- Remove bowl from heat. Using electric hand mixer (or in a stand mixer), beat on medium-high until bowl is no longer warm and meringue is stiff, 10 to 12 minutes. Add butter cubes, 1 at a time, and beat on medium until light and fluffy, 5 minutes longer. Beat in coconut and vanilla extracts.
- Stack cakes, using ¾ cup icing between layers. Cover cake with remaining icing and decorate with coconut chips.