Preheat the oven to 350 degrees F. Grease and flour 2 (9-inch) diameter cake pans and line the bottom with parchment.
Combine the flour, baking powder, baking soda and 1/2 teaspoon salt in a medium bowl. Whisk to combine.
In a separate large bowl, beat the sugar, butter and coconut milk until fluffy, about 3-5 minutes.
Beat in the egg yolks and vanilla extract.
With the mixer on low speed, beat in half the dry ingredients, followed by the milk, and the remaining dry ingredients, and the coconut, scraping down the sides in between each addition, just until blended.
Using clean, dry beaters, beat the egg whites with a pinch of salt in another clean large bowl until the egg whites are stiff but not dry.
In batches, fold the beaten egg whites into the batter, being careful not to deflate the whites. Divide the cake batter evenly between the prepared cake pans. Spread the batter with an offset spatula to level the batter in the pan.
Bake the cakes for 40 to 45 minutes, until a tester inserted into center comes out clean. Cool the cakes in the pans on a wire rack, about 10 minutes. Gently run a small sharp knife around the pan sides to loosen the cakes. Turn the cakes out onto cooling racks and cool completely.