Preheat oven to 350°F (175°C). Grease and line the bottoms of three 8-inch (or two 9-inch) round cake pans with parchment paper.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, using a hand mixer or stand mixer with the paddle attachment, beat the softened butter and sugar together on medium-high speed for 3-4 minutes, until light, pale, and fluffy.

Add the egg whites one at a time, beating well after each addition. Then add the two whole eggs, one at a time, beating until fully incorporated. Scrape down the bowl. Mix in the vanilla and coconut extracts.

In a measuring cup or small bowl, whisk together the coconut milk and buttermilk.

With the mixer on low speed, add the dry ingredients in three parts, alternating with the coconut milk/buttermilk mixture in two parts, beginning and ending with the dry ingredients. Mix only until just combined. Do not overmix.

Gently fold in the 1 cup of shredded coconut with a spatula.

Divide the batter evenly between the prepared pans. Bake for 25-30 minutes, or until a wooden skewer inserted into the center comes out clean.

Let the cakes cool in their pans for 15 minutes before turning them out onto a wire rack to cool completely. The cakes must be completely cool before frosting.

In a heatproof bowl, whisk together the egg whites, sugar, cold water, and corn syrup (or cream of tartar).

Place the bowl over a simmering water bath. Using a hand mixer, beat the mixture constantly on medium-high speed for exactly 7 minutes.

Remove the bowl from the heat. Beat in the vanilla extract and pinch of salt. Continue to beat for another 1-2 minutes.

Layer one cooled cake layer on your serving plate. Spread a generous amount of frosting over the top. Repeat with the remaining layers.

Apply a thin layer of frosting over the entire cake to create a 'crumb coat.' Place the cake in the refrigerator for 15 minutes to set.

Apply the remaining frosting in swoops and swirls to the top and sides of the cake.

Gently press and pat the remaining shredded coconut onto the sides and top of the cake until it’s fully covered.