Preheat oven to 350ºF and line two 9-inch round cake pans with greased parchment paper rounds (DO NOT grease the sides); set aside.
Transfer the yolks into the bowl of a stand mixer; set the whites aside.
In a small bowl, combine ½ cup granulated sugar and coconut flakes; mix well.
Add to yolks and, using the whisk attachment, process on medium speed at first and slowly increase to medium-high. Mix until the yolks become fluffy and thick, their color turns into a light yellow and when lifting the whisk from the bowl, the batter falls back in a ribbon, about 8 minutes.
Add 2 tbsp. milk and coconut extract. Process on medium speed until just combined.
Spoon the yolk mixture into a large bowl and set aside for now.
Clean the bowl and whisk attachment very well before adding egg whites and cream of tartar. Process on medium-high speed for 5 minutes or until soft peaks form.
Gradually add the remaining ½ cup of sugar and blend well before adding more.
When sugar is all mixed in, continue to process until stiff peaks form; set aside.
Working in batches, add sifted self-rising flour to a sifter. Sift it again into the yolk mixture (sifting twice will give a lighter and fluffier texture to the cake), stirring well between each addition. If the batter gets too thick, add a little bit of milk, maybe ½ tbsp. at the most, enough to finish mixing the batter properly.
Working in batches, add egg white mixture to the batter and gently fold until well incorporated before adding more (DO NOT OVERMIX).
Evenly divide the batter between the prepared cake pans and smooth out the tops using an angle spatula or the back of a spoon.
Transfer to the preheated oven and bake for 27 to 30 minutes or until a cake tester inserted in the center comes out clean.
Carefully remove the pans from the heat and place them on a wire rack; partially cool them for 20 minutes.
Flip the cake pans onto the wire rack and let them cool, upside down, for another 20 minutes.
Run a butter knife or an angle spatula around to loosen the cakes from the pans, discard the parchment rounds, and let them cool completely for 1 hour, sitting upside down on the wire rack.
Meanwhile make the Cream Cheese Frosting… (click here for directions)