This is from Dorie Greenspan's book "Baking From My Home to Yours." I made this for a cooking group I used to be a part of and it's delicious! This can be stored in the refrigerator for two days, but tastes best at room temperature.
Center a rack in the oven and preheat to 350°F Butter two 9" cake pans and line bottoms with parchment paper rounds. Place on baking sheet.
Sift together the cake flour, baking powder, and salt.
In a separate, medium-sized bowl, whisk together the egg whites and milk.
In another bowl, whisk together the lemon zest and sugar until fragrant. Or, you may rub the lemon zest and sugar together until fragrant.
Add the butter to the sugar and lemon zest mixture and beat at medium speed for three minutes or until butter and sugar are light.
Incorporate the extract and 1/3 flour mixture.
Beat in half the milk/egg mixture and beat in half of the remaining flour mixture.
Add the rest of the milk/egg mixture, then add in the rest of the dry ingredients.
Beat for at least two more minutes until all the ingredients are fully incorporated and the batter is well aerated.
Divide the batter evenly between the two pans and smooth tops with a rubber spatula.
Bake for 30-35 minutes until the cake is springy to the touch or a toothpick inserted comes out clean. Cook for about 5 minutes in the pan, then invert and cool on wire racks the rest of the way.
For the buttercream:
Put the sugar and egg whites in a double boiler, or heatproof bowl over a pot of simmering water. Whisk constantly, keeping the mixture over the heat, until it feels hot to the touch, or about 3 minutes. (Sugar will be dissolved and it will look like shiny marshmallow creme.).
Remove the bowl from the heat.
Beat with a whisk on medium speed for about 5 minutes. If using an electric mixer, switch to paddle attachment and add butter one stick at a time, beating until smooth. You will need to beat it for about 6-10 minutes after all the butter is incorporated. The mixture may separate, but keep beating, it will come back together.
While still beating at medium speed, gradually add the lemon juice, then the vanilla (be sure each addition is incorporated before adding more).
To store, press a piece of plastic over it.
For the Assembly:
Using a bread knife, level the top of each cake, then cut horizontally into two layers.
Lay down one layer of cake on a cake round. Spread 1/3 preserves, then 1/4 buttercream.
Repeat layers 1-3 until last layer of cake, which is placed upside down.
Cover the cake with the remaining buttercream, then coat with coconut.