Heat oven to 350º F (176º C).
Prepare two 8-inch (or 9-inch) cake pans by greasing them with butter (or vegetable oil), fitting parchment paper to the bottom of the pans, greasing the parchment paper, and lightly flouring the pans, getting rid of the excess flour.
To medium-sized mixing bowl, whisk the egg whites with the whole milk, and vanilla. Set aside.
To a large mixing bowl, add 2 ¼ cups of the cake flour (or the homemade cake flour).
Add the sugar, baking powder, and sea salt. Whisk together to combine.
Cut the butter into pieces and add it into the mixture. Use a spatula to incorporate the butter before using a mixer to completely combine.
Add half of the wet ingredients right into the dry ingredients and use an electric mixer to combine. Add the remaining wet ingredients and beat for another minute to incorporate.
Use a spatula to fold in the coconut flakes.
Pour batter evenly between the prepared cake pans and bake for 27-30 minutes or until toothpick inserted into the cake comes out clean.
Rest cakes for 10 minutes before removing them onto a cooling rack to completely cool.